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.

A358543 a(n) is the smallest number with exactly n divisors that are square pyramidal numbers.

Original entry on oeis.org

1, 5, 30, 140, 420, 1540, 4620, 13860, 78540, 157080, 471240, 1141140, 3603600, 3423420, 13693680, 30630600, 58198140, 116396280, 214414200, 428828400, 581981400, 1163962800, 5354228880, 4073869800, 8147739600, 26771144400, 36082846800, 80313433200, 93699005400, 187398010800
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

Comments

Any terms for n > 25 exceed 10^10. - Lucas A. Brown, Dec 24 2022
a(25) <= 8147739600, a(26) <= 26771144400, a(27) <= 36082846800, a(28) <= 80313433200. - Jon E. Schoenfield, Dec 16 2022

Examples

			a(3) = 30 because 30 has 3 square pyramidal divisors {1, 5, 30} and this is the smallest such number.

Links

Crossrefs

Cf. A000330, A005179, A130279, A279496, A358542, A358545.

Programs

  • PARI
    issqpyr(n) = my(m = sqrtnint(3*n, 3)); n==m*(m+1)*(2*m+1)/6; \\ A253903
a(n) = my(k=1); while (sumdiv(k, d, issqpyr(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(15) from Michel Marcus, Nov 21 2022
a(16)-a(20) from Jinyuan Wang, Nov 28 2022
a(21)-a(22) from Lucas A. Brown, Dec 14 2022
a(23)-a(24) from Lucas A. Brown, Dec 18 2022
a(25) from Lucas A. Brown, Dec 22 2022
a(26)-a(30) from Bert Dobbelaere, May 18 2025

A358544 a(n) is the smallest number with exactly n divisors that are centered triangular numbers.

Original entry on oeis.org

1, 4, 20, 320, 460, 5440, 14260, 12920, 168640, 103360, 594320, 3878720, 2377280, 9211960, 18423920, 36847840, 125995840, 73695680, 865924240, 976467760, 1952935520, 3463696960, 3905871040, 31246968320, 22946992360
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

Comments

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

Examples

			a(3) = 20 because 20 has 3 centered triangular divisors {1, 4, 10} and this is the smallest such number.

Links

Crossrefs

Cf. A005179, A005448, A130317, A300409, A358542, A358545.

Programs

  • PARI
    isct(n) = my(k=(2*n-2)/3, m); (n==1) || ((denominator(k)==1) && (m=sqrtint(k)) && (m*(m+1)==k)); \\ A005448
a(n) = my(k=1); while (sumdiv(k, d, isct(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(14) from Michel Marcus, Nov 21 2022
a(15)-a(25) from Jinyuan Wang, Nov 29 2022

A358540 a(n) is the smallest number with exactly n divisors that are n-gonal pyramidal numbers.

Original entry on oeis.org

56, 140, 1440, 11550, 351120, 41580, 742560, 29279250, 8316000, 72348396120, 3386892600, 578918340
Offset: 3

Views

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

Comments

Any subsequent terms are > 2 * 10^9. - Lucas A. Brown, Dec 24 2022

Examples

			a(5) = 1440 because 1440 has 5 pentagonal pyramidal divisors {1, 6, 18, 40, 288} and this is the smallest such number.

Links

Crossrefs

Cf. A005179, A358539, A358541, A358542, A358543.

Extensions

a(11)-a(13) from Martin Ehrenstein, Dec 02 2022
a(14) from Lucas A. Brown, Dec 19 2022
Showing 1-3 of 3 results.

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