A120359 - OEIS

A120359

Even refactorable numbers k such that the number r of odd divisors is odd, the number s of even divisors is even, both r and s are divisors of k and k is the first number for which the triple (r,s,t) occurs, where t is the number of divisors of k.

36, 3600, 8100, 10000, 26244, 32400, 142884, 202500, 396900, 518400, 656100, 810000, 1587600, 1679616, 2286144, 2624400, 3572100, 6350400, 9144576, 9922500, 12960000, 14288400, 20575296, 25401600, 28579716, 32148900, 39690000, 41990400, 48024900, 57153600, 89302500

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OFFSET

1,1

COMMENTS

Note that s is necessarily a multiple of r.

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

a(1) = 36 since r = 3, s = 6 and t = r+s = 9.

MATHEMATICA

seq[kmax_] := Module[{triples = {}, v = {}, r, s, t}, Do[t = DivisorSigma[0, k]; r = t - DivisorSigma[0, k/2]; s = t - r; If[OddQ[r] && EvenQ[s] && FreeQ[triples, {r, s, t}] && Divisible[k, t] && Divisible[k, r] && Divisible[k, s], AppendTo[v, k]; AppendTo[triples, {r, s, t}]], {k, 2, kmax, 2}]; v]; seq[10^6] (* Amiram Eldar, Aug 01 2024 *)

CROSSREFS

Cf. A000005, A001227, A033950, A049439, A057265, A120358, A120361, A183063.

Sequence in context: A364175 A209267 A120349 * A194611 A165984 A297021

Adjacent sequences: A120356 A120357 A120358 * A120360 A120361 A120362

KEYWORD

nonn

AUTHOR

Walter Kehowski, Jun 25 2006

EXTENSIONS

a(21)-a(22) inserted and a(24)-a(31) added by Amiram Eldar, Aug 01 2024

STATUS

approved