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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A358539 a(n) is the smallest number with exactly n divisors that are n-gonal numbers.

Original entry on oeis.org

6, 36, 210, 1260, 6426, 3360, 351000, 207900, 3749460, 1153152, 15036840, 204204000, 213825150, 11737440, 91797866160, 1006485480, 2310808500, 4966241280, 22651328700, 325269404460, 14266470332400, 11203920000, 256653797400, 45843256859400, 59207908359600, 46822406400
Offset: 3

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Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

Examples

			a(5) = 210 because 210 has 5 pentagonal divisors {1, 5, 35, 70, 210} and this is the smallest such number.

Links

Crossrefs

Cf. A005179, A130279, A130317, A356132, A358540, A358541.

Programs

  • PARI
    a(n) = my(k=1); while (sumdiv(k, d, ispolygonal(d, n)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(12)-a(13) from Michel Marcus, Nov 21 2022
a(14)-a(16) from Daniel Suteu, Dec 04 2022
a(17)-a(28) from Martin Ehrenstein, Dec 05 2022

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

Original entry on oeis.org

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

Views

Author

Bernard Schott, Jul 28 2022

Keywords

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
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