cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

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

A358541 a(n) is the smallest number with exactly n divisors that are centered n-gonal numbers.

Original entry on oeis.org

20, 325, 912, 43771, 234784, 11025, 680680, 9143308361, 2470852896
Offset: 3

Views

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

Comments

Any subsequent terms are > 10^10. - Lucas A. Brown, Dec 24 2022

Examples

			a(5) = 912 because 912 has 5 centered pentagonal divisors {1, 6, 16, 76, 456} and this is the smallest such number.

Links

Crossrefs

Cf. A005179, A358539, A358540, A358544, A358545.

Extensions

a(10)-a(11) from Martin Ehrenstein, Dec 04 2022

A358860 a(n) is the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers.

Original entry on oeis.org

56, 140, 4200, 331800, 611520, 8385930, 1071856800, 41086892000, 78540000, 38102655397426620, 59089382788800, 22241349900, 2326493030400, 7052419469195100, 886638404171520
Offset: 3

Views

Author

Ilya Gutkovskiy, Dec 03 2022

Keywords

Comments

The corresponding indices of n-gonal pyramidal numbers are 6, 7, 20, 79, 90, 203, ...

Examples

			a(4) = 140, because 140 is a square pyramidal number that has 4 square pyramidal divisors {1, 5, 14, 140} and this is the smallest such number.

Links

Crossrefs

Cf. A005179, A358540, A358859, A358861.

Programs

  • PARI
    pyramidal(k,r)=(k*(k+1)*((r-2)*k + (5-r)))\6;
ispyramidal(n, r) = pyramidal(sqrtnint(6*n\(r-2) + sqrtnint(n, 3), 3), r) == n;
a(n) = if(n<3, return()); for(k=1, oo, my(t=pyramidal(k,n)); if(sumdiv(t, d, ispyramidal(d, n)) == n, return(t))); \\ Daniel Suteu, Dec 06 2022

Extensions

a(9)-a(17) from Daniel Suteu, Dec 06 2022
Showing 1-3 of 3 results.

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