OFFSET

1,1

COMMENTS

Let 24*k+1 = p_1^e_1 * ... * p_r^e_r * q_1^f_1 * ... * q_s^f_s, where the p_i's are distinct primes == 1, 5, 7, or 11 (mod 24) and the q_i's are distinct primes == 13, 17, 19, or 23 (mod 24). Then k belongs to the sequence iff all of the f_i's are even and all but one of the e_i's are even and the one e_i which is odd is == 1 (mod 4). - Dean Hickerson, Jan 19 2006

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Krishnaswami Alladi, Partition Identities Involving Gaps and Weights, Transactions of the American Mathematical Society, Vol. 349, No. 12 (Dec 1997), pp. 5001-5019.

MATHEMATICA

q[n_] := Module[{f = FactorInteger[n], f1, f2}, f1 = Select[f, MemberQ[{1, 5, 7, 11}, Mod[First[#], 24]] &]; f2 = Select[f, MemberQ[{13, 17, 19, 23}, Mod[First[#], 24]] &]; AllTrue[f2[[;; , 2]], EvenQ] && Count[f1[[;; , 2]], _?OddQ] == 1]; Select[Range[160], q[24 * # + 1] &] (* Amiram Eldar, Aug 24 2024 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 06 2006

STATUS

approved