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A175418
Complement of A175397, where A175397 = numbers such that both arithmetic means of distinct and all prime factors are not integers.
2
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
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
KEYWORD
nonn,changed
AUTHOR
Jaroslav Krizek, May 09 2010
EXTENSIONS
a(49) corrected by Robert Israel, Nov 10 2024
STATUS
approved