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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
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. A006881, A054753, A085986 (seem to be subsequences).
Sequence in context: A299992 A237051 A340749 * A325281 A100658 A182301
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.)