

A296205


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


2



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

Table of n, a(n) for n=1..73.


FORMULA

a(n) = A000196(A296204(n)).


CROSSREFS

Cf. A000196, A295666, A296204.
Cf. A006881, A054753, A085986 (seem to be subsequences).
Cf. A004709, A007774, A056239, A112798, A118914, A307370, A325240.
Sequence in context: A084227 A299992 A237051 * A325281 A100658 A182301
Adjacent sequences: A296202 A296203 A296204 * A296206 A296207 A296208


KEYWORD

nonn


AUTHOR

Antti Karttunen, Dec 18 2017


STATUS

approved



