0,2

(2n+1)^2 divides a(2n). a(2n)/(2n+1)^2 = {1,1,41,5713,1657009,826446281,633095889817,691413758034721,...} = A081215(2n). p divides a(p-1) for prime p. a(p-1)/p = {1,3,205,39991,9090909091,8230246567621,...} = A081209(p-1) = A076951(p-1). p^2 divides a(p-1) for an odd prime p. a(p-1)/p^2 = {1,41,5713,826446281,633095889817,1021273028302258913,1961870762757168078553, 14199269001914612973017444081,...} = A081215(p-1). Prime p divides a((p-3)/2) for p = {13,17,19,23,37,41,43,47,61,67,71,89,109,113,137,139,157,163,167,181,191,...}. Prime p divides a((p-5)/4) for p = {29,41,61,89,229,241,281,349,421,509,601,641,661,701,709,769,809,821,881,...} = A107218(n) Primes of the form 4x^2+25y^2. Prime p divides a((p-7)/6) for p = {79,109,127,151,313,421,541,601,613,751,757,787,...}. Prime p divides a((p-9)/8) for p = {41,337,401,521,569,577,601,857,929,937,953,977,...} A subset of A007519(n) Primes of form 8n+1. Prime p divides a((p-11)/10) for p = {41,181,331,601,761,1021,1151,1231,1801,...}. Prime p divides a((p-13)/12) for p = {313,337,433,1621,1873,1993,2161,2677,2833,...}.

a(n) = n^(n+1) + 1. a(n) = A007778(n) + 1.

Table[n^(n+1)+1, {n, 0, 30}]

Cf. A007778 - n^(n+1). Cf. A000312 - n^n. Cf. A014566 - Sierpinski numbers of the first kind: n^n + 1. Cf. A081209, A076951, A081215.

Sequence in context: A147302 A112670 A117581 this_sequence A006040 A067309 A087798

Adjacent sequences: A123567 A123568 A123569 this_sequence A123571 A123572 A123573

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 12 2006