A267891 Numbers with 8 odd divisors.

105, 135, 165, 189, 195, 210, 231, 255, 270, 273, 285, 297, 330, 345, 351, 357, 375, 378, 385, 390, 399, 420, 429, 435, 455, 459, 462, 465, 483, 510, 513, 540, 546, 555, 561, 570, 594, 595, 609, 615, 621, 627, 645, 651, 660, 663, 665, 690, 702, 705, 714, 715, 741, 750, 756, 759, 770, 777, 780, 783, 795, 798, 805, 837

Offset: 1

Author

Omar E. Pol, Apr 03 2016

Keywords

• nonn

Comments

Positive integers that have exactly eight odd divisors.

Numbers n such that the symmetric representation of sigma(n) has 8 subparts. - Omar E. Pol, Dec 29 2016

Numbers n such that A000265(n) has prime signature {7} or {3,1} or {1,1,1}, i.e., is in A092759 or A065036 or A007304. - Robert Israel, Mar 15 2018

Numbers that can be formed in exactly 7 ways by summing sequences of 2 or more consecutive positive integers. - Julie Jones, Aug 13 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Column 8 of A266531.

Cf. A000265, A001227, A007304, A038547, A065036, A092759, A237593, A279387.

Numbers with exactly k odd divisors (k = 1..10): A000079, A038550, A072502, apparently A131651, A267696, A230577, A267697, this sequence, A267892, A267893.

Programs

Magma

[n: n in [1..1000] | #[d: d in Divisors(n) | IsOdd(d)] eq 8]; // Bruno Berselli, Apr 04 2016

Maple

filter:= proc(n) local r;
  r:= n/2^padic:-ordp(n,2);
  numtheory:-tau(r)=8
end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 15 2018

Mathematica

Select[Range@ 840, Length@ Select[Divisors@ #, OddQ] == 8 &] (* Michael De Vlieger, Dec 30 2016 *)

PARI

isok(n) = sumdiv(n, d, (d%2)) == 8; \\ after Michel Marcus

Formula

A001227(a(n)) = 8.