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%I #8 Dec 27 2022 16:01:46
%S 1,5,22,12,210,176,1520,1080,8400,55200,273280,43776,2624832,7173360,
%T 71660160,100659200,34255872,178962432,3623854080,17895751680,
%U 5413478400,43690752000,927712542720,733008101376,1789570252800,35917382287360,50649120571392
%N Smallest pentagonal number with n prime factors (counted with multiplicity).
%C Pentagonal analogy of A075088.
%t 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
%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 *)
%Y Cf. A075088, A209048.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Mar 04 2012
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