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.

A271319 Number of distinct prime factors of the n-th n-gonal number (A060354).

Original entry on oeis.org

1, 2, 1, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 4, 2, 2, 3, 4, 3, 3, 3, 3, 3, 2, 4, 3, 3, 2, 5, 3, 2, 4, 3, 4, 3, 2, 4, 4, 4, 3, 4, 3, 3, 3, 3, 4, 3, 2, 4, 4, 4, 2, 4, 4, 3, 4, 3, 3, 4, 4, 3, 5, 2, 3, 4, 4, 4, 4, 4, 3, 4, 2, 4, 5, 3, 3, 4, 3, 4, 3, 4, 4, 5, 4, 3, 4
Offset: 2

Views

Author

Colin Barker, Apr 04 2016

Keywords

Examples

			a(7) = 2 because A060354(7) = 112 = 2^4 * 7^1.

Links

Crossrefs

Cf. A001221, A060354, A271320, A271321, A271322.

Programs

  • Mathematica
    Table[PrimeNu[PolygonalNumber[n,n]],{n,2,90}] (* Harvey P. Dale, Sep 24 2023 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = omega(pg(n, n))
vector(100, n, n++; a(n))

Formula

a(n) = A001221(A060354(n)).

A271320 Number of prime factors, with multiplicity, of the n-th n-gonal number (A060354).

Original entry on oeis.org

1, 2, 4, 2, 3, 5, 5, 3, 3, 3, 7, 2, 3, 5, 6, 3, 4, 4, 6, 3, 3, 5, 6, 3, 4, 5, 9, 2, 5, 4, 7, 4, 4, 4, 7, 2, 4, 9, 7, 3, 4, 3, 7, 4, 3, 5, 7, 3, 5, 4, 7, 2, 6, 6, 6, 4, 3, 3, 9, 4, 3, 7, 8, 3, 4, 4, 7, 4, 4, 6, 8, 2, 4, 6, 7, 3, 4, 4, 8, 6, 4, 4, 8, 4, 3, 6
Offset: 2

Views

Author

Colin Barker, Apr 04 2016

Keywords

Examples

			a(7) = 5 because A060354(7) = 112 = 2^4 * 7^1.

Links

Crossrefs

Cf. A001222, A060354, A271319, A271321, A271322.

Programs

  • Mathematica
    PrimeOmega/@Table[PolygonalNumber[n,n],{n,90}] (* Harvey P. Dale, Feb 08 2025 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = bigomega(pg(n, n))
vector(100, n, n++; a(n))

Formula

a(n) = A001222(A060354(n)).

A271321 Smallest prime factor of the n-th n-gonal number (A060354).

Original entry on oeis.org

2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 13, 2, 2, 2, 11, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 2, 29, 2, 2, 2, 3, 2, 2, 2, 37, 2, 2, 2, 11, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 53, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 73, 2, 2, 2, 7, 2, 2, 2, 3, 2, 2, 2, 5
Offset: 2

Views

Author

Colin Barker, Apr 04 2016

Keywords

Examples

			a(5) = 5 because A060354(5) = 35 = 5 * 7.

Links

Crossrefs

Cf. A020639, A060354, A271319, A271320, A271322.

Programs

  • Mathematica
    Table[FactorInteger[PolygonalNumber[n,n]][[1,1]],{n,2,90}] (* Harvey P. Dale, Feb 26 2022 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
spf(m) = factorint(m)[1, 1] \\ Smallest prime factor
a(n) = spf(pg(n, n))
vector(100, n, n++; a(n))

Formula

a(n) = A020639(A060354(n)).
Showing 1-3 of 3 results.

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

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