A267891 - OEIS

%I #42 Sep 08 2022 08:46:15

%S 105,135,165,189,195,210,231,255,270,273,285,297,330,345,351,357,375,

%T 378,385,390,399,420,429,435,455,459,462,465,483,510,513,540,546,555,

%U 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

%N Numbers with 8 odd divisors.

%C Positive integers that have exactly eight odd divisors.

%C Numbers n such that the symmetric representation of sigma(n) has 8 subparts. - _Omar E. Pol_, Dec 29 2016

%C 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

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

%H Robert Israel, <a href="/A267891/b267891.txt">Table of n, a(n) for n = 1..10000</a>

%F A001227(a(n)) = 8.

%p filter:= proc(n) local r;

%p   r:= n/2^padic:-ordp(n,2);

%p   numtheory:-tau(r)=8

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Mar 15 2018

%t Select[Range@ 840, Length@ Select[Divisors@ #, OddQ] == 8 &] (* _Michael De Vlieger_, Dec 30 2016 *)

%o (PARI) isok(n) = sumdiv(n, d, (d%2)) == 8; \\ after _Michel Marcus_

%o (Magma) [n: n in [1..1000] | #[d: d in Divisors(n) | IsOdd(d)] eq 8]; // _Bruno Berselli_, Apr 04 2016

%Y Column 8 of A266531.

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

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

%K nonn

%O 1,1

%A _Omar E. Pol_, Apr 03 2016