A387918 - OEIS

A387918

Positive integers whose number of divisors is a power of an odd prime.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 169, 196, 225, 256, 289, 361, 441, 484, 529, 625, 676, 729, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1681, 1764, 1849, 2116, 2209, 2304, 2401, 2601, 2809, 3025, 3249, 3364, 3481, 3721, 3844, 4096, 4225

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OFFSET

1,2

COMMENTS

After a(1), first differs from A384517 at n = 40. a(40) = 2304 = 2^8 * 3^2 is not a term of A384517. Also, A384517(92) = 16384 = 2^14 is the least term in A384517 that is not a term in this sequence.

Numbers k such that A000005(k) is in A061345.

Numbers whose prime factorization exponents are of the form p^k - 1 with the same prime p and any k >= 1.

LINKS

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

FORMULA

Sum_{n>=1} 1/a(n) = 1 + Sum_{q prime} Product_{p prime} (Sum_{k >= 0} 1/p^(q^k-1)) = 1.62106031221236818383... .

MATHEMATICA

q[k_] := OddQ[k] && (k == 1 || PrimePowerQ[k]); Select[Range[12000], q[DivisorSigma[0, #]] &]

PROG

(PARI) isok(k) = if(k == 1, 1, my(d = numdiv(k)); d % 2 && isprimepower(d));

CROSSREFS

A036454 is a subsequence.