A279497 -id:A279497 - cp's OEIS frontend

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

Bernard Schott, Jul 28 2022

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, ...

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

Cf. A000326, A279497, A356132.

Similar sequences: A046952, A093036, A350756, A355595.

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 *)

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

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

A356132 Least integer with n pentagonal divisors.

Original entry on oeis.org

1, 5, 35, 70, 210, 420, 2310, 4620, 18480, 32340, 60060, 120120, 240240, 720720, 1261260, 1141140, 2042040, 4084080, 4564560, 13693680, 19399380, 58198140, 95855760, 38798760, 116396280, 193993800, 77597520, 232792560, 543182640, 387987600, 1125164040

Offset: 1

Michel Marcus, Jul 27 2022

nonn

Rémy Sigrist, C program

Cf. A000326, A130317, A279497.

C
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See Links section.
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a(n) = my(k=1); while (sumdiv(k, d, ispolygonal(d, 5)) != n, k++); k;

More terms from Rémy Sigrist, Jul 27 2022

A334924 G.f.: Sum_{k>=1} x^(k^2(k + 1)/2) / (1 - x^(k^2(k + 1)/2)).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1

Offset: 1

Ilya Gutkovskiy, May 16 2020

nonn

Number of pentagonal pyramidal numbers (A002411) dividing n.

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number.

Cf. A002411, A007862, A195055, A279495, A279496, A279497.

nmax = 100; CoefficientList[Series[Sum[x^(k^2 (k + 1)/2)/(1 - x^(k^2 (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi^2/3 - 2 = A195055 - 2 = 1.289868... . - Amiram Eldar, Jan 02 2024

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

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A356132 Least integer with n pentagonal divisors.

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PARI

Extensions

A334924 G.f.: Sum_{k>=1} x^(k^2(k + 1)/2) / (1 - x^(k^2(k + 1)/2)).

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cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions

A356132 Least integer with n pentagonal divisors.

Views

Author

Keywords

Links

Crossrefs

Programs

C

PARI

Extensions

A334924 G.f.: Sum_{k>=1} x^(k^2*(k + 1)/2) / (1 - x^(k^2*(k + 1)/2)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A334924 G.f.: Sum_{k>=1} x^(k^2(k + 1)/2) / (1 - x^(k^2(k + 1)/2)).