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A375960
Numbers whose product of proper divisors is a cube.
2
1, 2, 3, 5, 7, 8, 11, 13, 16, 17, 19, 23, 24, 27, 29, 30, 31, 37, 40, 41, 42, 43, 47, 53, 54, 56, 59, 61, 64, 66, 67, 70, 71, 73, 78, 79, 81, 83, 88, 89, 97, 101, 102, 103, 104, 105, 107, 109, 110, 113, 114, 125, 127, 128, 130, 131, 135, 136, 137, 138, 139, 149
OFFSET
1,2
COMMENTS
Wells erroneously writes that the smallest number on this list should be 24.
All the primes are in this list since they have the only proper divisor 1 which is trivially a cube.
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 101.
LINKS
EXAMPLE
16 is a term since 1*2*4*8 = 64 = 4^3.
MATHEMATICA
Select[Range[150], IntegerQ[Product[Part[Divisors[#], i], {i, DivisorSigma[0, #]-1}]^(1/3)] &]
PROG
(PARI) isok(k) = my(d=divisors(k)); ispower(vecprod(Vec(d, #d-1)), 3); \\ Michel Marcus, Sep 04 2024
CROSSREFS
Cf. A000040 (subsequence), A000578, A007956, A027751, A032741.
Complement of A375962.
Sequence in context: A051600 A319239 A331050 * A026410 A066720 A079851
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Sep 04 2024
STATUS
approved