

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.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Note that s is necessarily a multiple of r.


LINKS



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



KEYWORD

nonn


AUTHOR



EXTENSIONS

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


STATUS

approved



