A358263 Numbers with a record number of noninfinitary square divisors.

1, 16, 144, 256, 1296, 2304, 20736, 57600, 331776, 518400, 2822400, 8294400, 12960000, 25401600, 132710400, 207360000, 228614400, 406425600, 635040000, 2057529600, 3073593600, 6502809600, 10160640000, 27662342400, 31116960000, 51438240000, 76839840000, 248961081600

Offset

1,2

Comments

Numbers m such that A358261(m) > A358261(k) for all k < m.

The corresponding record values are 0, 1, 2, 3, 5, 6, 11, 12, 13, 22, 24, 26, 37, 44, 46, 47, 48, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..187

Amiram Eldar, Table of n, a(n), A358261(a(n)) for n = 1..187

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; s = {}; fmax = -1; Do[If[(fn = f[n]) > fmax, fmax = fn; AppendTo[s, n]], {n, 1, 6*10^5}]; s

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(nmax) = {my(smax = -1, sn); for(n = 1, nmax, sn = s(n); if(sn > smax, smax = sn; print1(n, ", "))); }

Crossrefs

Cf. A358261, A358262.

Subsequence of A025487.

Similar sequences: A002182, A002110 (unitary), A037992 (infinitary), A293185, A306736, A307845, A309141, A318278, A322484, A335386, A348632, A358253.

Sequence in context: A336239 A332105 A032444 * A358262 A328224 A017114

Adjacent sequences: A358260 A358261 A358262 * A358264 A358265 A358266

Keyword

nonn

Author

Amiram Eldar, Nov 06 2022

Status

approved