A285510 -id:A285510 - cp's OEIS frontend

A303480 Numbers k such that the average of squarefree kernels of all positive integers <= k is an integer.

1, 3, 4, 17, 53, 433, 456, 901, 1052, 4011, 14504, 15111, 156408, 245423, 328408, 911340, 2263141, 13736475, 20092485, 37903271, 60003559, 78733423, 84206981, 234095587, 319691535, 986119609, 1488787296, 6139123252, 8663152552, 11909530004, 19226378456, 65827587400

Offset: 1

Ilya Gutkovskiy, Apr 24 2018

nonn

Numbers k such that k | A073355(k).

			3 is a term because the first 3 terms of A007947 are 1, 2 and 3 whose sum is divisible by 3.

Wikipedia, Radical of an integer

Cf. A007947, A073355, A226647, A284755, A285510.

isok(k) = sum(i=1, k, factorback(factor(i)[, 1])) % k == 0; \\ Michel Marcus, Apr 25 2018

a(13)-a(17) from Alois P. Heinz, Apr 24 2018
a(18)-a(26) from Daniel Suteu, Apr 24 2018
a(27)-a(32) from Giovanni Resta, Apr 26 2018

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

Original entry on oeis.org

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

Ilya Gutkovskiy, May 17 2017

nonn

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

			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.

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

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

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

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

cp's OEIS Frontend

A303480 Numbers k such that the average of squarefree kernels of all positive integers <= k is an integer.

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