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A271320 Number of prime factors, with multiplicity, of the n-th n-gonal number (A060354).

%I A271320 #13 Feb 08 2025 17:41:07
%S A271320 1,2,4,2,3,5,5,3,3,3,7,2,3,5,6,3,4,4,6,3,3,5,6,3,4,5,9,2,5,4,7,4,4,4,
%T A271320 7,2,4,9,7,3,4,3,7,4,3,5,7,3,5,4,7,2,6,6,6,4,3,3,9,4,3,7,8,3,4,4,7,4,
%U A271320 4,6,8,2,4,6,7,3,4,4,8,6,4,4,8,4,3,6
%N A271320 Number of prime factors, with multiplicity, of the n-th n-gonal number (A060354).
%H A271320 Colin Barker, <a href="/A271320/b271320.txt">Table of n, a(n) for n = 2..1000</a>
%F A271320 a(n) = A001222(A060354(n)).
%e A271320 a(7) = 5 because A060354(7) = 112 = 2^4 * 7^1.
%t A271320 PrimeOmega/@Table[PolygonalNumber[n,n],{n,90}] (* _Harvey P. Dale_, Feb 08 2025 *)
%o A271320 (PARI)
%o A271320 pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
%o A271320 a(n) = bigomega(pg(n, n))
%o A271320 vector(100, n, n++; a(n))
%Y A271320 Cf. A001222, A060354, A271319, A271321, A271322.
%K A271320 nonn
%O A271320 2,2
%A A271320 _Colin Barker_, Apr 04 2016