A209049 Smallest pentagonal number with n prime factors (counted with multiplicity).

1, 5, 22, 12, 210, 176, 1520, 1080, 8400, 55200, 273280, 43776, 2624832, 7173360, 71660160, 100659200, 34255872, 178962432, 3623854080, 17895751680, 5413478400, 43690752000, 927712542720, 733008101376, 1789570252800, 35917382287360, 50649120571392

Offset: 0

Author

Robert G. Wilson v, Mar 04 2012

Keywords

• nonn

Comments

Pentagonal analogy of A075088.

Crossrefs

Cf. A075088, A209048.

Programs

Mathematica

k = 1; t = Table[0, {50}]; While[k < 500000001, a = PrimeOmega[k] + PrimeOmega[3 k - 1] - 1; If[ t[[a + 1]] == 0, t[[a + 1]] = k; Print[{k, a}]]; k++]; # (3 # - 1)/2 & /@ t
Join[{1},Table[SelectFirst[{#,PrimeOmega[#]}&/@PolygonalNumber[5,Range[ 110000]],#[[2]]==n&],{n,20}][[All,1]]] (* The program generates the first 21 terms of the sequence. *) (* Harvey P. Dale, Dec 27 2022 *)