A358262 - OEIS

%I #10 Nov 07 2022 02:10:35

%S 1,16,144,256,3600,1296,2304,65536,129600,16777216,32400,20736,57600,

%T 331776,589824,4294967296,6350400,1099511627776,150994944,810000,

%U 1587600,1679616,518400,5308416,2822400,84934656,8294400,26873856,14745600,21743271936,38654705664

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

%C a(n) is the least number k such that A358261(k) = n.

%C Since A358261(k) depends only on the prime signature of k, all the terms of this sequence are in A025487.

%H Amiram Eldar, <a href="/A358262/b358262.txt">Table of n, a(n) for n = 0..50</a>

%e a(1) = 16 since 16 is the least number with exactly one noninfinitary divisor, 4.

%t 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 (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 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. A025487, A358261, A358263.

%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), A358252 (non-unitary square).

%K nonn

%O 0,2

%A _Amiram Eldar_, Nov 06 2022