A303482 Numbers k such that the average of all distinct prime factors of all positive integers <= k is an integer.

2, 5, 81, 10742, 10130527, 1041972864, 23292549600

Offset: 1

Author

Ilya Gutkovskiy, Apr 24 2018

Keywords

• nonn
• more

Comments

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

Examples

			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
		

Links

• Eric Weisstein's World of Mathematics, Distinct Prime Factors

Crossrefs

Cf. A001221, A008472, A013939, A024924, A078174, A078175, A226647, A284755, A303480.

Programs

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 *)

Extensions

a(5) from Daniel Suteu, Apr 24 2018

a(6)-a(7) from Giovanni Resta, Apr 26 2018