

A303482


Numbers k such that the average of all distinct prime factors of all positive integers <= k is an integer.


2




OFFSET

1,1


COMMENTS

Numbers k such that A013939(k)A024924(k).


LINKS

Table of n, a(n) for n=1..7.
Eric Weisstein's World of Mathematics, Distinct Prime Factors


EXAMPLE

5 is in the sequence because the distinct prime factors of 2, 3, 4, and 5 are 2, 3, 2 and 5 respectively and their average (2 + 3 + 2 + 5) / 4 = 3 is an integer.  David A. Corneth, Apr 26 2018


MATHEMATICA

s = t = 0; k = 2; lst = {}; While[k < 1000000000, p = #[[1]] & /@ FactorInteger@ k; s = s + Plus @@ p; t = t + Length@ p; If[ Mod[s, t] == 0, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Apr 26 2018 *)


CROSSREFS

Cf. A001221, A008472, A013939, A024924, A078174, A078175, A226647, A284755, A303480.
Sequence in context: A127997 A096266 A123978 * A290952 A201113 A309089
Adjacent sequences: A303479 A303480 A303481 * A303483 A303484 A303485


KEYWORD

nonn,more


AUTHOR

Ilya Gutkovskiy, Apr 24 2018


EXTENSIONS

a(5) from Daniel Suteu, Apr 24 2018
a(6)a(7) from Giovanni Resta, Apr 26 2018


STATUS

approved



