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A267891 Numbers with 8 odd divisors. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

FORMULA

A001227(a(n)) = 8.

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 *)

PROG

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

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

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.

Sequence in context: A095643 A206265 A253022 * A097217 A115935 A069702

Adjacent sequences:  A267888 A267889 A267890 * A267892 A267893 A267894

KEYWORD

nonn

AUTHOR

Omar E. Pol, Apr 03 2016

STATUS

approved

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Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)