A267696 Numbers with 5 odd divisors.

81, 162, 324, 625, 648, 1250, 1296, 2401, 2500, 2592, 4802, 5000, 5184, 9604, 10000, 10368, 14641, 19208, 20000, 20736, 28561, 29282, 38416, 40000, 41472, 57122, 58564, 76832, 80000, 82944, 83521, 114244, 117128, 130321, 153664, 160000, 165888, 167042, 228488, 234256, 260642, 279841

Offset

1,1

Comments

Positive integers that have exactly five odd divisors.

Numbers k such that the symmetric representation of sigma(k) has 5 subparts. - Omar E. Pol, Dec 28 2016

Also numbers that can be expressed as the sum of k > 1 consecutive positive integers in exactly 4 ways; e.g., 81 = 40+41 = 26+27+28 = 11+12+13+14+15+16 = 5+6+7+8+9+10+11+12+13. - Julie Jones, Aug 13 2018

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

A001227(a(n)) = 5.

Sum_{n>=1} 1/a(n) = 2 * P(4) - 1/8 = 0.00289017370127..., where P(4) is the value of the prime zeta function at 4 (A085964). - Amiram Eldar, Sep 16 2024

Prog

(PARI) isok(n) = sumdiv(n, d, (d%2)) == 5; \\ Michel Marcus, Apr 03 2016
(GAP) A:=List([1..700000], n->DivisorsInt(n));;
B:=List([1..Length(A)], i->Filtered(A[i], IsOddInt));;
a:=Filtered([1..Length(B)], i->Length(B[i])=5); # Muniru A Asiru, Aug 14 2018

Crossrefs

Column 5 of A266531.

Cf. A001227, A030514, A038547, A085964, A236104, A237593, A279387.

Numbers with k odd divisors (k = 1..10): A000079, A038550, A072502, apparently A131651, this sequence, A230577, A267697, A267891, A267892, A267893.

Sequence in context: A044632 A031494 A043324 * A232923 A250655 A184003

Adjacent sequences: A267693 A267694 A267695 * A267697 A267698 A267699

Keyword

nonn

Author

Omar E. Pol, Apr 03 2016

Extensions

More terms from Michel Marcus, Apr 03 2016

Status

approved