A358263 -id:A358263 - cp's OEIS frontend

A358262 a(n) is the least number with exactly n noninfinitary square divisors.

1, 16, 144, 256, 3600, 1296, 2304, 65536, 129600, 16777216, 32400, 20736, 57600, 331776, 589824, 4294967296, 6350400, 1099511627776, 150994944, 810000, 1587600, 1679616, 518400, 5308416, 2822400, 84934656, 8294400, 26873856, 14745600, 21743271936, 38654705664

Offset: 0

Amiram Eldar, Nov 06 2022

nonn

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

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

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

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

Cf. A025487, A358261, A358263.

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).

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]

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])))};
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

A358262 a(n) is the least number with exactly n noninfinitary square divisors.

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