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

1, 4, 12, 16, 60, 36, 48, 256, 360, 4096, 180, 144, 240, 576, 768, 65536, 2520, 1048576, 12288, 900, 1260, 1296, 720, 2304, 1680, 9216, 2880, 5184, 3840, 147456, 196608, 36864, 27720, 46656, 3145728, 4398046511104, 61440, 3600, 6300, 18014398509481984, 10080, 20736

Offset

0,2

Comments

a(n) is the least number k such that A348341(k) = n.

Since A348341(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..50

Example

a(1) = 4 since 4 is the least number with exactly one noninfinitary divisor, 2.

Mathematica

f[1] = 0; f[n_] := DivisorSigma[0, n] - Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[;; , 2]]];
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[35, 10^7]

Prog

(PARI) s(n) = {my(f = factor(n)); numdiv(f) - prod(i = 1, #f~, 2^hammingweight(f[i, 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. A025487, A348341, A348342.

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).

Sequence in context: A239413 A351893 A327295 * A066632 A038242 A370191

Adjacent sequences: A361415 A361416 A361417 * A361419 A361420 A361421

Keyword

nonn

Author

Amiram Eldar, Mar 11 2023

Status

approved