

A212918


Numbers whose sum of prime factors (counted with multiplicity) is a pentagonal number (A000326).


1



1, 5, 6, 35, 42, 50, 57, 60, 64, 72, 81, 85, 102, 121, 124, 182, 188, 201, 232, 260, 261, 267, 308, 312, 351, 440, 452, 495, 519, 528, 594, 645, 649, 688, 735, 741, 774, 784, 805, 854, 861, 875, 882, 901, 966, 1025, 1027, 1045, 1050, 1081, 1105, 1112, 1119
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OFFSET

1,2


COMMENTS

This is to pentagonal numbers A000326 as A000290 squares are to A212831 numbers whose sum of prime factors is a square (counted with multiplicity) and as A000217 triangular numbers are to A212849 Numbers whose sum of prime factors (counted with multiplicity) is a triangular number.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000


FORMULA

{k such that A001414(k) = sopfr(k) is in A000326(j) = j*(3*j1)/2 for some integer j}.


EXAMPLE

a(3) = 35 because sopfr(35) = sum of prime factors of 35 = 5 + 7 = 12, and 12 is the 3rd pentagonal number.


MATHEMATICA

pentagonalQ[n_] := IntegerQ[(1 + Sqrt[1 + 24*n])/6]; pfs[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; Dot[p, e]]; Select[Range[1500], pentagonalQ[pfs[#]] &] (* T. D. Noe, May 31 2012 *)


PROG

(PARI) sopfr(n) = my(f=factor(n)); sum(k=1, matsize(f)[1], f[k, 1]*f[k, 2]); \\ A001414
isok(n) = ispolygonal(sopfr(n), 5); \\ Michel Marcus, May 02 2018


CROSSREFS

Cf. A000326, A001414, A212831, A212849.
Sequence in context: A151506 A122008 A248254 * A255197 A253192 A036254
Adjacent sequences: A212915 A212916 A212917 * A212919 A212920 A212921


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, May 31 2012


EXTENSIONS

Corrected by T. D. Noe, May 31 2012


STATUS

approved



