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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. 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 (list; graph; refs; listen; history; text; internal format)
 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 Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000196(A296204(n)). 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: select(filter, [\$1..200]); # Robert Israel, Feb 20 2024 CROSSREFS Cf. A000196, A295666, A296204. Cf. A006881, A054753, A085986 (seem to be subsequences). Cf. A004709, A007774, A056239, A112798, A118914, A307370, A325240. Sequence in context: A299992 A237051 A340749 * A325281 A100658 A182301 Adjacent sequences: A296202 A296203 A296204 * A296206 A296207 A296208 KEYWORD nonn AUTHOR Antti Karttunen, Dec 18 2017 STATUS approved

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Last modified June 19 00:02 EDT 2024. Contains 373490 sequences. (Running on oeis4.)