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

Author

Amiram Eldar, Nov 06 2022

Keywords

• nonn

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

Crossrefs

Cf. A358261, A358262.

Subsequence of A025487.

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

Programs

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

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, ", "))); }