login
A361418
a(n) is the least number with exactly n noninfinitary divisors.
1
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
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 11 2023
STATUS
approved