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

1,1

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

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

Crossrefs

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

Sequence in context: A360613 A293205 A046687 * A078175 A213715 A360552

Adjacent sequences: A175415 A175416 A175417 * A175419 A175420 A175421

Keyword

nonn

Author

Jaroslav Krizek, May 09 2010

Extensions

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

Status

approved