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

Author

Omar E. Pol, Apr 03 2016

Keywords

• nonn

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

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.

Programs

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

PARI

isok(n) = sumdiv(n, d, (d%2)) == 5; \\ Michel Marcus, Apr 03 2016

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

Extensions

More terms from Michel Marcus, Apr 03 2016