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.

A260234 Largest prime factor of the n-th hexagonal number (A000384).

Original entry on oeis.org

3, 5, 7, 5, 11, 13, 5, 17, 19, 11, 23, 13, 7, 29, 31, 17, 7, 37, 13, 41, 43, 23, 47, 7, 17, 53, 11, 29, 59, 61, 7, 13, 67, 23, 71, 73, 19, 13, 79, 41, 83, 43, 29, 89, 23, 47, 19, 97, 11, 101, 103, 53, 107, 109, 37, 113, 29, 59, 17, 61, 41, 7, 127, 43, 131
Offset: 2

Views

Author

Colin Barker, Jul 20 2015

Keywords

Comments

As A000384(n+1) = (n*2+1)*(n*1+1), A000384(n) belongs to A180045 for n > 3, and a(n) tends to infinity as n tends to infinity. - Rémy Sigrist, Feb 23 2020

Examples

			a(3) = 5 because A000384(3) = 15 = 3 * 5.

Links

Crossrefs

Cf. A000384, A006530, A180045, A260233, A260235, A260236.

Programs

  • Mathematica
    FactorInteger[#][[-1,1]]&/@PolygonalNumber[6,Range[2,70]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 10 2018 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
lpf(m) = vecmax(factorint(m)[, 1]) \\ Largest prime factor
a(n) = lpf(pg(6, n))

Formula

a(n) = A006530(A000384(n)).

A260235 Number of distinct prime factors of the n-th hexagonal number (A000384).

Original entry on oeis.org

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

Views

Author

Colin Barker, Jul 20 2015

Keywords

Examples

			a(6) = 3 because A000384(6) = 66 = 2 * 3 * 11.

Links

Crossrefs

Cf. A000384, A001221, A260233, A260234, A260236.

Programs

  • Mathematica
    PrimeNu[PolygonalNumber[6,Range[2,90]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 23 2017 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = omega(pg(6, n))

Formula

a(n) = A001221(A000384(n)).

A260236 Number of prime factors, with multiplicity, of the n-th hexagonal number (A000384).

Original entry on oeis.org

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

Views

Author

Colin Barker, Jul 20 2015

Keywords

Examples

			a(4) = 3 because A000384(4) = 28 = 2^2 * 7.

Links

Crossrefs

Cf. A000384, A001222, A260233, A260234, A260235.

Programs

  • Mathematica
    Rest[PrimeOmega[PolygonalNumber[6,Range[90]]]] (* Harvey P. Dale, Aug 10 2021 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = bigomega(pg(6, n))

Formula

a(n) = A001222(A000384(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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