Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Nov 04 2024 20:48:21
%S 1,2,6,30,210,1680,2310,18480,30030,240240,480480,3843840,4084080,
%T 8168160,65345280,77597520,155195040,1241560320,1784742960,3569485920,
%U 28555887360,51757545840,103515091680,828120733440,1604483921040,3208967842080,25671742736640,51343485473280
%N Numbers k that have a record number of divisors d such that gcd(d, k/d) is a square.
%C Indices of records in A365171.
%C The corresponding record values are 1, 2, 4, 8, 16, 24, 32, 48, 64, 96, ... (see the link for more values).
%H Amiram Eldar, <a href="/A377707/b377707.txt">Table of n, a(n) for n = 1..102</a>
%H Amiram Eldar, <a href="/A377707/a377707.txt">Table of n, a(n), A365171(a(n)) for n = 1..102</a>
%t f[p_, e_] := Floor[(e + 3)/4] + Floor[(e + 4)/4]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n]; v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq
%Y Cf. A365171.
%Y Subsequence of A025487.
%K nonn
%O 1,2
%A _Amiram Eldar_, Nov 04 2024