A348342 -id:A348342 - cp's OEIS frontend

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

Amiram Eldar, Mar 11 2023

nonn

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.

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

Amiram Eldar, Table of n, a(n) for n = 0..50

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).

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]

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};

cp's OEIS Frontend

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

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