A286972 Numbers k such that the average of the prime power divisors (not including 1) of k is an integer.

2, 3, 4, 5, 7, 9, 11, 12, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 42, 43, 47, 49, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73, 75, 77, 78, 79, 80, 81, 83, 84, 85, 87, 89, 91, 93, 95, 97, 100, 101, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 119, 121, 123, 127, 129, 131, 132, 133, 135, 137, 139

Offset: 1

Author

Ilya Gutkovskiy, May 17 2017

Keywords

• nonn

Comments

Numbers k such that A001222(k)|A023889(k).

Examples

			12 is in the sequence because 12 has 6 divisors {1, 2, 3, 4, 6, 12} among which 3 are prime powers {2, 3, 4} and (2 + 3 + 4)/3 = 3 is an integer.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A001222, A003601, A023886, A023889, A078174, A246655, A285510.

Programs

Mathematica

fQ[n_] := IntegerQ@Mean@Select[Divisors@n, PrimePowerQ]; Select[Range@140, fQ]

PARI

isok(m) = my(vd = select(isprimepower, divisors(m))); #vd && !(vecsum(vd) % #vd); \\ Michel Marcus, Apr 28 2020