A175418 Complement of A175397, where A175397 = numbers such that both arithmetic means of distinct and all prime factors are not integers.

2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 20, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 42, 43, 44, 45, 47, 49, 50, 51, 53, 55, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 73, 75, 77, 78, 79, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 99

Offset: 1

Author

Jaroslav Krizek, May 09 2010

Keywords

• nonn

Comments

For these numbers hold that both arithmetic means of distinct and all prime factors are integers or only one of these means is an integer.

Includes all prime powers and odd semiprimes. - Robert Israel, Nov 10 2024

Links

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

Crossrefs

Cf. A174894, A176552, A175352, A175397, A176587.

Programs

Maple

filter:= proc(n) local F,t;
  F:= ifactors(n)[2];
  (add(t[1],t=F)/nops(F))::integer or (add(t[1]*t[2],t=F)/add(t[2],t=F))::integer
end proc:
select(filter, [$2..100]); # Robert Israel, Nov 10 2024

Extensions

a(49) corrected by Robert Israel, Nov 10 2024