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a(n) = Sum_{k=0..n} binomial(n, k) * Sum_{j=k..n} n!/(k!*(j - k)!). Row sums of A377661.
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1, 3, 14, 80, 534, 4102, 35916, 354888, 3915750, 47754938, 637840356, 9256590928, 144977618044, 2436460447020, 43719637179224, 834042701945520, 16852447379512710, 359468276129261730, 8070500634880125300, 190211302604157871680, 4695001374741310892820
a(n) is the least prime p such that (3^p - 3)/p == n (mod p), or -1 if there is no such prime p.
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11, 2, 3, 5, 7, 23, 43, 5721619, 2311, 105830189, 31300663, 13, 113, 17, 821, 1181, 19, 37
Number of subwords of the form UDD in nondecreasing Dyck paths of length 2n.
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0, 0, 1, 4, 14, 45, 138, 411, 1200, 3454, 9836, 27779, 77938, 217493, 604222, 1672246, 4613030, 12689265, 34817418, 95320335, 260436588, 710278318, 1933906496, 5257545599, 14273273314, 38699274665, 104799960058, 283487736166, 766045036730, 2067997219629, 5577597593466, 15030365074659, 40470488092008
Number of prime factors of n^n+n (counted with multiplicity).
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1, 2, 3, 4, 3, 5, 6, 7, 4, 7, 4, 5, 4, 8, 6, 8, 5, 7, 11, 7, 6, 10, 6, 8, 7, 10, 10, 12, 6, 7, 11, 11, 7, 13, 7, 11, 8, 7, 5, 12, 7, 7, 13, 9, 10, 18, 6, 11, 11, 11, 11, 12, 10, 11, 14, 14, 12, 11, 7, 10, 13, 7, 8, 21, 5, 14, 10, 8, 7, 15, 11, 10, 13, 8, 9, 17
a(n) is the number of divisors of n^n + n.
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2, 4, 8, 12, 8, 32, 48, 48, 12, 128, 16, 24, 16, 256, 64, 80, 32, 96, 1536, 96, 64, 1024, 64, 96, 96, 512, 512, 3072, 64, 128, 2048, 384, 128, 8192, 128, 1152, 256, 128, 32, 2048, 128, 128, 6144, 288, 768, 262144, 64, 480, 1536, 1536, 2048, 3072, 1024, 1024
a(n) is the sum of the divisors of n^n + n.
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3, 12, 72, 588, 5652, 117504, 1895712, 46503600, 839411118, 25440307200, 474527311344, 22404560101168, 489294047662728, 30902868417576960, 1096805935992340800, 38000593697802058224, 1318965178069293272496, 90596485743469636057920, 3578317312662511683264000
a(n) = phi(n^n + n) where phi is the Euler totient function.
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1, 2, 8, 96, 1248, 12000, 259200, 5461344, 129140160, 2725643520, 127561104000, 2743415522496, 139778722137600, 2504616361228800, 111747349423990784, 8644660582219776000, 387774574486565683200, 12306643656809728412160, 816897235219321957908480
Number of prime factors of n^n-n (counted with multiplicity).
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1, 4, 5, 7, 5, 9, 7, 12, 8, 9, 7, 13, 6, 11, 17, 16, 6, 17, 7, 15, 10, 10, 10, 19, 11, 18, 15, 14, 7, 22, 13, 21, 11, 14, 22, 24, 7, 15, 15, 26, 9, 20, 7, 17, 17, 12, 11, 30, 9, 24, 15, 20, 10, 29, 16, 27, 12, 13, 9, 29, 8, 18, 29, 27, 15, 24, 8, 23, 13, 25
a(n) is the number of divisors of n^n - n.
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2, 8, 18, 40, 24, 120, 48, 336, 80, 192, 72, 1920, 48, 288, 23040, 1728, 36, 10240, 72, 7680, 432, 240, 384, 32256, 640, 49152, 2016, 3840, 96, 193536, 1152, 22528, 1152, 4608, 1327104, 1638400, 96, 7680, 9216, 4128768, 384, 294912, 72, 23040, 30720, 576
a(n) is the sum of the divisors of n^n - n.
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3, 60, 728, 10416, 116064, 2837120, 36990720, 1452853584, 27615698352, 965243666880, 23861701899840, 1355882884941312, 20758574413420992, 1604569397488307712, 93340493714183159808, 3135286584767445151680, 90560273718863022770592, 8284620870197084160000000
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