cp's OEIS Frontend

A358262 a(n) is the least number with exactly n noninfinitary square divisors.

%I A358262 #10 Nov 07 2022 02:10:35
%S A358262 1,16,144,256,3600,1296,2304,65536,129600,16777216,32400,20736,57600,
%T A358262 331776,589824,4294967296,6350400,1099511627776,150994944,810000,
%U A358262 1587600,1679616,518400,5308416,2822400,84934656,8294400,26873856,14745600,21743271936,38654705664
%N A358262 a(n) is the least number with exactly n noninfinitary square divisors.
%C A358262 a(n) is the least number k such that A358261(k) = n.
%C A358262 Since A358261(k) depends only on the prime signature of k, all the terms of this sequence are in A025487.
%H A358262 Amiram Eldar, <a href="/A358262/b358262.txt">Table of n, a(n) for n = 0..50</a>
%e A358262 a(1) = 16 since 16 is the least number with exactly one noninfinitary divisor, 4.
%t A358262 f1[p_, e_] := 1 + Floor[e/2]; f2[p_, e_] := 2^DigitCount[If[OddQ[e], e - 1, e], 2, 1]; f[1] = 0; f[n_] := Times @@ f1 @@@ (fct = FactorInteger[n]) - Times @@ f2 @@@ fct; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[15, 2*10^7]
%o A358262 (PARI) s(n) = {my(f = factor(n));  prod(i=1, #f~, 1+f[i,2]\2) - prod(i=1, #f~, 2^hammingweight(if(f[i,2]%2, f[i,2]-1, f[i,2])))};
%o A358262 lista(len, nmax) = {my(v = vector(len), c = 0, n = 1, i); while(c < len && n < nmax, i = s(n) + 1; if(i <= len && v[i] == 0, c++; v[i] = n); n++); v};
%Y A358262 Cf. A025487, A358261, A358263.
%Y A358262 Similar sequences: A005179 (all divisors), A038547 (odd divisors), A085629 (coreful divisors), A130279 (square), A187941 (even), A309181 (non-unitary), A340232 (bi-unitary), A340233 (exponential), A357450 (odd square), A358252 (non-unitary square).
%K A358262 nonn
%O A358262 0,2
%A A358262 _Amiram Eldar_, Nov 06 2022