A388971 Positive numbers whose factorial has more exponential divisors than all smaller factorials.

1, 4, 6, 10, 15, 16, 18, 20, 24, 25, 28, 30, 34, 35, 39, 46, 54, 60, 63, 64, 69, 78, 88, 92, 99, 102, 106, 111, 114, 116, 126, 130, 142, 150, 156, 158, 164, 165, 166, 180, 188, 189, 190, 202, 205, 222, 226, 228, 230, 232, 246, 250, 264, 272, 273, 276, 284, 285

Offset

1,2

Comments

Indices of records in A388840.

All the terms are nonprimes.

a(n)-1 is a term in A388843 for n >= 2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..3000

Example

The first 6 terms in A388840 are 1, 1, 1, 2, 2, and 6. The record values, 1, 2, and 6, occur at positions 1, 4, and 6, the first 3 terms in this sequence.

Mathematica

d[n_] := Times @@ (DivisorSigma[0, Last[#]] & /@ FactorInteger[n!]);
seq[nmax_] := Module[{s = {}, dmax = 0, d1}, Do[d1 = d[n]; If[d1 > dmax, AppendTo[s, n]; dmax = d1], {n, 1, nmax}]; s]; seq[100]

Prog

(PARI) d(n) = vecprod(apply(numdiv, factor(n!)[, 2]));
list(nmax) = {my(dmax = 0, d1); for(n = 1, nmax, d1 = d(n); if(d1 > dmax, dmax = d1; print1(n, ", "))); }

Crossrefs

Cf. A000142, A049419, A388840, A388843.

Sequence in context: A084372 A353543 A388014 * A140611 A333846 A076957

Adjacent sequences: A388968 A388969 A388970 * A388972 A388973 A388974

Keyword

nonn

Author

Amiram Eldar, Sep 22 2025

Status

approved