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A296205 Numbers k such that Product_{d|k^2, gcd(d,k^2/d) is prime} gcd(d,k^2/d) = k^2.

%I A296205 #25 Feb 20 2024 14:44:21
%S A296205 1,6,10,12,14,15,18,20,21,22,26,28,33,34,35,36,38,39,44,45,46,50,51,
%T A296205 52,55,57,58,62,63,65,68,69,74,75,76,77,82,85,86,87,91,92,93,94,95,98,
%U A296205 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
%N A296205 Numbers k such that Product_{d|k^2, gcd(d,k^2/d) is prime} gcd(d,k^2/d) = k^2.
%C A296205 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
%H A296205 Robert Israel, <a href="/A296205/b296205.txt">Table of n, a(n) for n = 1..10000</a>
%F A296205 a(n) = A000196(A296204(n)).
%p A296205 filter:= proc(k) local d,r,v;
%p A296205    r:= 1;
%p A296205    for d in numtheory:-divisors(k^2) do
%p A296205      v:= igcd(d,k^2/d);
%p A296205      if isprime(v) then r:= r*v fi
%p A296205    od;
%p A296205    r = k^2
%p A296205 end proc:
%p A296205 select(filter, [$1..200]); # _Robert Israel_, Feb 20 2024
%Y A296205 Cf. A000196, A295666, A296204.
%Y A296205 Cf. A006881, A054753, A085986 (seem to be subsequences).
%Y A296205 Cf. A004709, A007774, A056239, A112798, A118914, A307370, A325240.
%K A296205 nonn
%O A296205 1,2
%A A296205 _Antti Karttunen_, Dec 18 2017