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.

A358861 a(n) is the smallest centered n-gonal number divisible by exactly n centered n-gonal numbers.

Original entry on oeis.org

64, 925, 2976, 93457, 866272, 11025, 3036880, 18412718645101, 9283470627432, 201580440699781, 92839099743040, 5236660451226975, 66779973961058176
Offset: 3

Views

Author

Ilya Gutkovskiy, Dec 03 2022

Keywords

Comments

a(17) = 1415913990579036. - Daniel Suteu, Dec 10 2022

Examples

			a(5) = 2976, because 2976 is a centered pentagonal number that has 5 centered pentagonal divisors {1, 6, 16, 31, 2976} and this is the smallest such number.

Links

Crossrefs

Cf. A005179, A358541, A358859, A358860.

Programs

  • PARI
    a(n) = if(n<3, return()); for(k=1, oo, my(t=((n*k*(k+1))/2+1)); if(sumdiv(t, d, issquare(8*(d-1)/n + 1) && (sqrtint((8*(d-1))/n + 1)-1)%2 == 0) == n, return(t))); \\ Daniel Suteu, Dec 10 2022

Extensions

a(10)-a(15) from Daniel Suteu, Dec 06 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

A358058 a(n) is the index of the smallest n-gonal number divisible by exactly n n-gonal numbers.

Original entry on oeis.org

3, 6, 12, 48, 51, 330, 1100, 702, 8120, 980, 5499, 110880, 10472, 2688, 2127411, 517104, 710640, 396480, 2761803, 4254120, 13347975, 707000, 3655827
Offset: 3

Views

Author

Ilya Gutkovskiy, Dec 12 2022

Keywords

Links

Crossrefs

Cf. A358859.
Showing 1-3 of 3 results.

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

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