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

0,2

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.

Links

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

Example

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

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]

Prog

(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};

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).

Sequence in context: A357789 A363333 A358253 * A374159 A325839 A379593

Adjacent sequences: A358249 A358250 A358251 * A358253 A358254 A358255

Keyword

nonn

Author

Amiram Eldar, Nov 05 2022

Status

approved