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A361418 a(n) is the least number with exactly n noninfinitary divisors.

%I A361418 #9 Mar 12 2023 04:20:44
%S A361418 1,4,12,16,60,36,48,256,360,4096,180,144,240,576,768,65536,2520,
%T A361418 1048576,12288,900,1260,1296,720,2304,1680,9216,2880,5184,3840,147456,
%U A361418 196608,36864,27720,46656,3145728,4398046511104,61440,3600,6300,18014398509481984,10080,20736
%N A361418 a(n) is the least number with exactly n noninfinitary divisors.
%C A361418 a(n) is the least number k such that A348341(k) = n.
%C A361418 Since A348341(k) depends only on the prime signature of k, all the terms of this sequence are in A025487.
%H A361418 Amiram Eldar, <a href="/A361418/b361418.txt">Table of n, a(n) for n = 0..50</a>
%e A361418 a(1) = 4 since 4 is the least number with exactly one noninfinitary divisor, 2.
%t A361418 f[1] = 0; f[n_] := DivisorSigma[0, n] - Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[;; , 2]]];
%t A361418 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];
%t A361418 seq[35, 10^7]
%o A361418 (PARI) s(n) = {my(f = factor(n)); numdiv(f) - prod(i = 1, #f~, 2^hammingweight(f[i,2]));}
%o A361418 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 A361418 Cf. A025487, A348341, A348342.
%Y A361418 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 A361418 nonn
%O A361418 0,2
%A A361418 _Amiram Eldar_, Mar 11 2023