login
A358262
a(n) is the least number with exactly n noninfinitary square divisors.
3
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
0,2
COMMENTS
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.
LINKS
EXAMPLE
a(1) = 16 since 16 is the least number with exactly one noninfinitary divisor, 4.
MATHEMATICA
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]
PROG
(PARI) 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};
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: A332105 A032444 A358263 * A328224 A017114 A331741
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 06 2022
STATUS
approved