A358252 - OEIS

%I #14 Nov 06 2022 03:17:06

%S 1,8,32,128,288,864,1152,2592,4608,13824,10368,20736,28800,41472,

%T 64800,279936,115200,331776,345600,663552,259200,1679616,518400,

%U 1620000,1166400,4860000,1036800,17915904,2073600,15552000,6998400,26873856,4147200,53747712,8294400

%N a(n) is the least number with exactly n non-unitary square divisors.

%C a(n) is the least number k such that A056626(k) = n.

%C Since A056626(k) depends only on the prime signature of k, all the terms of this sequence are in A025487.

%H Amiram Eldar, <a href="/A358252/b358252.txt">Table of n, a(n) for n = 0..176</a>

%e a(1) = 8 since 8 is the least number that has exactly one non-unitary square divisor, 4.

%t f1[p_, e_] := 1 + Floor[e/2]; f2[p_, e_] := 2^(1 - Mod[e, 2]); 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[21, 10^6]

%o (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + floor(f[i,2]/2)) - 2^sum(i = 1, #f~, 1 - f[i,2]%2);}

%o 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 Cf. A056626, A025487, A358253.

%Y 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).

%K nonn

%O 0,2

%A _Amiram Eldar_, Nov 05 2022