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 1-4 of 4 results.

A358542 a(n) is the smallest number with exactly n divisors that are tetrahedral numbers.

Original entry on oeis.org

1, 4, 56, 20, 120, 280, 560, 840, 1680, 10920, 9240, 18480, 55440, 120120, 240240, 314160, 628320, 1441440, 2282280, 7225680, 4564560, 9129120, 13693680, 27387360, 54774720, 68468400, 77597520, 136936800, 155195040, 310390080, 465585120, 775975200, 1163962800
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

Examples

			a(3) = 56 because 56 has 3 tetrahedral divisors {1, 4, 56} and this is the smallest such number.

Links

Crossrefs

Cf. A000292, A005179, A130317, A279495, A358543, A358544.

Programs

  • PARI
    istetrah(n) = my(k=sqrtnint(6*n, 3)); k*(k+1)*(k+2)==6*n; \\ A000292
a(n) = my(k=1); while (sumdiv(k, d, istetrah(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(20)-a(22) from Michel Marcus, Nov 21 2022
a(23)-a(30) from Jinyuan Wang, Nov 28 2022
a(31) from Martin Ehrenstein, Dec 02 2022
a(32) and a(33) from Lucas A. Brown, Dec 14 2022

A358545 a(n) is the smallest number with exactly n divisors that are centered square numbers.

Original entry on oeis.org

1, 5, 25, 325, 1625, 1105, 5525, 27625, 160225, 1022125, 801125, 5928325, 8491925, 29641625, 42459625, 444215525, 314201225, 2003613625, 1571006125, 14826740825, 12882250225, 127081657625, 64411251125, 88717383625
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) = 25 because 25 has 3 centered square divisors {1, 5, 25} and this is the smallest such number.

Links

Crossrefs

Cf. A001844, A005179, A130279, A300410, A358543, A358544.

Programs

  • PARI
    iscsq(n) = issquare(2*n-1); \\ A001844
a(n) = my(k=1); while (sumdiv(k, d, iscsq(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(12)-a(15) from Michel Marcus, Nov 21 2022
a(16) from Martin Ehrenstein, Dec 02 2022
a(17)-a(24) from Jinyuan Wang, Dec 02 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

A359231 a(n) is the smallest centered triangular number divisible by exactly n centered triangular numbers.

Original entry on oeis.org

1, 4, 64, 5860, 460, 74260, 14260, 1221760, 5567104, 103360, 20120860, 169096960, 1211757760, 31286787760, 31498960, 114183284260, 1553569960, 33186496960, 446613160960, 43581101074960, 274644405760, 64262632960, 121634429663260, 5786547945760
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 22 2022

Keywords

Comments

a(25) > 10^15. a(30) = 281149511296960. - Jon E. Schoenfield, Dec 25 2022

Examples

			a(5) = 460, because 460 is a centered triangular number that has 5 centered triangular divisors {1, 4, 10, 46, 460} and this is the smallest such number.

Links

Crossrefs

Cf. A005448, A076983, A300409, A358544, A358861, A359232.

Programs

  • Magma
    // Note: the program below finds all terms through a(22) except for
//  a(20) = 43581101074960, which would be reached at k = 5390183.
a := [ 0 : n in [ 1 .. 22 ] ];
for k in [ 0 .. 550000 ] do
   c := 3*((k*(k - 1)) div 2) + 1;
   D := Divisors(c);
   n := 0;
   for d in D do
      if d mod 3 eq 1 then
         if IsSquare(((d - 1) div 3)*8 + 1) then
            n +:= 1;
         end if;
      end if;
   end for;
   if a[n] eq 0 then
      a[n] := c;
   end if;
end for;
a; // Jon E. Schoenfield, Dec 25 2022

Extensions

a(8)-a(24) from Jon E. Schoenfield, Dec 25 2022
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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