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A046659 Numbers whose sum of divisors and sum of cubes of divisors are relatively prime. 1
1, 4, 9, 25, 36, 100, 121, 225, 289, 484, 529, 841, 900, 1089, 1156, 1681, 2116, 2209, 2601, 2809, 3364, 3481, 4356, 4761, 5041, 6724, 6889, 7225, 7569, 7921, 8836, 10201, 10404, 11236, 11449, 12769, 13225, 13924, 15129, 17161, 18769, 19044 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that (a) all the numbers are squares, (b) the number of divisors is a power of 3.

It can be shown that this is a subset of A028982.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

k=100 has 9 divisors whose sum is 217 = 7*31 and whose sum of cubes is 1149823 = 19*73*829; gcd(217, 1149823) = 1, so 100 is in the sequence.

MATHEMATICA

Select[Range[20000], GCD[DivisorSigma[1, #], DivisorSigma[3, #]]==1&]  (* Harvey P. Dale, Feb 19 2011 *)

PROG

(PARI) isok(n) = gcd(sigma(n), sigma(n, 3)) == 1; \\ Michel Marcus, May 14 2018

CROSSREFS

Cf. A028982, A046679, A046680, A046681, A046683, A046685.

Sequence in context: A248648 A063577 A087058 * A063760 A238334 A130448

Adjacent sequences:  A046656 A046657 A046658 * A046660 A046661 A046662

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified September 18 23:16 EDT 2021. Contains 347548 sequences. (Running on oeis4.)