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Numbers k such that the average of squarefree kernels of all positive integers <= k is an integer.
3

%I #14 Apr 26 2018 07:47:36

%S 1,3,4,17,53,433,456,901,1052,4011,14504,15111,156408,245423,328408,

%T 911340,2263141,13736475,20092485,37903271,60003559,78733423,84206981,

%U 234095587,319691535,986119609,1488787296,6139123252,8663152552,11909530004,19226378456,65827587400

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

%C Numbers k such that k | A073355(k).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Radical_of_an_integer">Radical of an integer</a>

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

%o (PARI) isok(k) = sum(i=1, k, factorback(factor(i)[, 1])) % k == 0; \\ _Michel Marcus_, Apr 25 2018

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

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Apr 24 2018

%E a(13)-a(17) from _Alois P. Heinz_, Apr 24 2018

%E a(18)-a(26) from _Daniel Suteu_, Apr 24 2018

%E a(27)-a(32) from _Giovanni Resta_, Apr 26 2018