A267893 Numbers with 10 odd divisors.

405, 567, 810, 891, 1053, 1134, 1377, 1539, 1620, 1782, 1863, 1875, 2106, 2268, 2349, 2511, 2754, 2997, 3078, 3240, 3321, 3483, 3564, 3726, 3750, 3807, 4212, 4293, 4375, 4536, 4698, 4779, 4941, 5022, 5427, 5508, 5751, 5913, 5994, 6156, 6399, 6480, 6642, 6723, 6875, 6966, 7128, 7203, 7209, 7452, 7500, 7614, 7857, 8125

Offset: 1

Author

Omar E. Pol, Apr 03 2016

Keywords

• nonn

Comments

Positive integers that have exactly 10 odd divisors.

Numbers n such that the symmetric representation of sigma(n) has 10 subparts. - Omar E. Pol, Dec 29 2016

Numbers that can be formed in exactly 9 ways by summing sequences of 2 or more consecutive positive integers. - Julie Jones, Aug 13 2018

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..5000

Crossrefs

Column 10 of A266531.

Cf. A001227, A038547, A237593, A279387.

Numbers with exactly k odd divisors (k = 1..10): A000079, A038550, A072502, apparently A131651, A267696, A230577, A267697, A267891, A267892, this sequence.

Programs

GAP

A:=List([1..10000],n->DivisorsInt(n));; B:=List([1..Length(A)],i->Filtered(A[i],IsOddInt));;
a:=Filtered([1..Length(B)],i->Length(B[i])=10); # Muniru A Asiru, Aug 14 2018

Mathematica

Select[Range@ 8125, Length@ Select[Divisors@ #, OddQ] == 10 &] (* Michael De Vlieger, Dec 30 2016 *)

PARI

isok(n) = sumdiv(n, d, (d%2)) == 10; \\ after Michel Marcus

Formula

A001227(a(n)) = 10.