A356179 Positions of records in A279497, i.e., integers whose number of pentagonal divisors sets a new record.

1, 5, 35, 70, 210, 420, 2310, 4620, 18480, 32340, 60060, 120120, 240240, 720720, 1141140, 2042040, 4084080, 4564560, 13693680, 19399380, 38798760, 77597520, 232792560, 387987600

Offset: 1

Author

Bernard Schott, Jul 28 2022

Keywords

• nonn
• more

Comments

The first fourteen terms are the same as A356132; then a(15) = 1141140 while A356132(15) = 1261260.

Corresponding records of number of pentagonal divisors are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, ...

Examples

			210 is in the sequence because A279497(210) = 5 is larger than any earlier value in A279497.
		

Crossrefs

Cf. A000326, A279497, A356132.

Similar sequences: A046952, A093036, A350756, A355595.

Programs

Mathematica

f[n_] := DivisorSum[n, 1 &, IntegerQ[(1 + Sqrt[1 + 24*#])/6] &]; fm = -1; s = {}; Do[If[(fn = f[n]) > fm, fm = fn; AppendTo[s, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Jul 28 2022 *)

PARI

lista(nn) = my(m=0); for (n=1, nn, my(new = sumdiv(n, d, ispolygonal(d, 5))); if (new > m, m = new; print1(n, ", "));); \\ Michel Marcus, Jul 28 2022

Extensions

a(23)-a(24) from David A. Corneth, Jul 28 2022