A137489 Numbers with 26 divisors.

12288, 20480, 28672, 45056, 53248, 69632, 77824, 94208, 118784, 126976, 151552, 167936, 176128, 192512, 217088, 241664, 249856, 274432, 290816, 299008, 323584, 339968, 364544, 397312, 413696, 421888, 438272, 446464, 462848, 520192, 536576

Offset

1,1

Comments

Maple implementation: see A030513.

Numbers of the form p^25 (5th powers of A050997, subset of A010813) or p*q^12, where p and q are distinct primes. - R. J. Mathar, Mar 01 2010

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

A000005(a(n))=26.

Mathematica

Select[Range[900000], DivisorSigma[0, #]==26&] (* Vladimir Joseph Stephan Orlovsky, May 05 2011 *)

Prog

(PARI) is(n)=numdiv(n)==26 \\ Charles R Greathouse IV, Jun 19 2016
(Python)
from sympy import integer_nthroot, primerange, primepi
from oeis_sequences.OEISsequences import bisection
def A137489(n):
    def f(x): return int(n+x-sum(primepi(x//p**12) for p in primerange(integer_nthroot(x, 12)[0]+1))+primepi(integer_nthroot(x, 13)[0])-primepi(integer_nthroot(x, 25)[0]))
    return bisection(f, n, n) # Chai Wah Wu, May 01 2026

Crossrefs

Cf. A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.

Sequence in context: A262625 A262623 A140688 * A233900 A172488 A133860

Adjacent sequences: A137486 A137487 A137488 * A137490 A137491 A137492

Keyword

nonn

Author

R. J. Mathar, Apr 22 2008

Status

approved