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

1,2

Comments

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

Links

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

Example

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

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

Crossrefs

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

Sequence in context: A363171 A336323 A175352 * A129493 A036350 A295076

Adjacent sequences: A175394 A175395 A175396 * A175398 A175399 A175400

Keyword

nonn,changed

Author

Jaroslav Krizek, May 01 2010

Extensions

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

Status

approved