A175397 Numbers such that both arithmetic means of distinct and all prime factors are not integers.

1, 6, 10, 12, 14, 18, 22, 24, 26, 28, 30, 34, 36, 38, 40, 46, 48, 52, 54, 56, 58, 62, 66, 70, 72, 74, 76, 80, 82, 86, 88, 90, 94, 96, 98, 100, 102, 104, 106, 108, 118, 120, 122, 124, 130, 132, 134, 136, 138, 142, 144, 146, 148, 150, 152, 154, 158, 160, 162, 165, 166, 172, 174, 176, 178, 182, 184

Offset: 1

Author

Jaroslav Krizek, May 01 2010

Keywords

• nonn

Comments

Contains all even semiprimes. - Robert Israel, Nov 10 2024

Examples

			For a(13) = 36: 36 = 2^2*3^3; both (2+2+3+3)/4 and (2+3)/2 are not integers.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A176552, A175352 and A176587. Complement of A175418. Cf. A174894.

Programs

Maple

filter:= proc(n) local F,t,m;
  F:= ifactors(n)[2]; m:= nops(F);
  not (add(t[1],t=F)/m)::integer and not (add(t[1]*t[2],t=F)/add(t[2],t=F))::integer
end proc:
filter(1):= true:
select(filter, [$1..1000]); # Robert Israel, Nov 10 2024

Extensions

a(27) corrected, and more terms from Robert Israel, Nov 10 2024