A358252 a(n) is the least number with exactly n non-unitary square divisors.

1, 8, 32, 128, 288, 864, 1152, 2592, 4608, 13824, 10368, 20736, 28800, 41472, 64800, 279936, 115200, 331776, 345600, 663552, 259200, 1679616, 518400, 1620000, 1166400, 4860000, 1036800, 17915904, 2073600, 15552000, 6998400, 26873856, 4147200, 53747712, 8294400

Offset: 0

Author

Amiram Eldar, Nov 05 2022

Keywords

• nonn

Comments

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

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

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 0..176

Crossrefs

Cf. A056626, A025487, A358253.

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).

Programs

Mathematica

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]

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);}
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};