

A296205


Numbers k such that Product_{dk^2, gcd(d,k^2/d) is prime} gcd(d,k^2/d) = k^2.


3



1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 26, 28, 33, 34, 35, 36, 38, 39, 44, 45, 46, 50, 51, 52, 55, 57, 58, 62, 63, 65, 68, 69, 74, 75, 76, 77, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 100, 106, 111, 115, 116, 117, 118, 119, 122, 123, 124, 129, 133, 134, 141, 142, 143, 145, 146, 147, 148, 153, 155, 158, 159, 161
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OFFSET

1,2


COMMENTS

Except for a(1) = 1, these appear to be cubefree numbers with two distinct prime factors, or Heinz numbers of integer partitions with two distinct parts, none appearing more than twice. The enumeration of these partitions by sum is given by A307370. Equivalently, except for a(1) = 1, this sequence is the intersection of A004709 and A007774.  Gus Wiseman, Jul 03 2019


LINKS



FORMULA



MAPLE

filter:= proc(k) local d, r, v;
r:= 1;
for d in numtheory:divisors(k^2) do
v:= igcd(d, k^2/d);
if isprime(v) then r:= r*v fi
od;
r = k^2
end proc:


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



