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

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

2,1

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Formula

a(n) = A020639(A060354(n)).

Example

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

Mathematica

Table[FactorInteger[PolygonalNumber[n, n]][[1, 1]], {n, 2, 90}] (* Harvey P. Dale, Feb 26 2022 *)

Prog

(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))

Crossrefs

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

Sequence in context: A232736 A275887 A121358 * A112659 A342550 A115281

Adjacent sequences: A271318 A271319 A271320 * A271322 A271323 A271324

Keyword

nonn

Author

Colin Barker, Apr 04 2016

Status

approved