OFFSET
1,2
COMMENTS
a(3) = 197 and a(11) = 538727822713277 are primes.
p divides a(p+1) for primes p > 3.
a(2*k-1) is odd. a(2*k) is even. a(2^k) is divisible by 2^(2*k - 1) for k > 0.
Numbers n such that a(n) is divisible by n are listed in A124240.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..100
FORMULA
a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k - 1)^m.
a(n) = n + Sum_{k=2..n} (2*k - 1)*((2*k - 1)^n - 1)/(2*(k - 1)).
MATHEMATICA
Table[Sum[(2k-1)^m, {k, 1, n}, {m, 1, n}], {n, 1, 20}]
PROG
(PARI) a(n) = sum(k=1, n, sum(m=1, n, (2*k - 1)^m)); \\ Michel Marcus, Apr 24 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Oct 22 2006
STATUS
approved