cp's OEIS Frontend

A325134 a(1) = 1; a(n) = number of prime factors of n counted with multiplicity plus the largest prime index of n.

%I A325134 #6 Apr 03 2019 05:19:34
%S A325134 1,2,3,3,4,4,5,4,4,5,6,5,7,6,5,5,8,5,9,6,6,7,10,6,5,8,5,7,11,6,12,6,7,
%T A325134 9,6,6,13,10,8,7,14,7,15,8,6,11,16,7,6,6,9,9,17,6,7,8,10,12,18,7,19,
%U A325134 13,7,7,8,8,20,10,11,7,21,7,22,14,6,11,7,9,23
%N A325134 a(1) = 1; a(n) = number of prime factors of n counted with multiplicity plus the largest prime index of n.
%C A325134 A prime index of n is a number m such that prime(m) divides n.
%C A325134 Also one plus the size of the largest hook contained in the Young diagram of the integer partition with Heinz number n. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%F A325134 a(n) = A001222(n) + A061395(n).
%F A325134 a(n) = A252464(n) + 1.
%p A325134 with(numtheory):
%p A325134 a:= n-> `if`(n=1, 1, bigomega(n)+pi(max(factorset(n)[]))):
%p A325134 seq(a(n), n=1..100);  # _Alois P. Heinz_, Apr 03 2019
%t A325134 Table[If[n==1,1,PrimeOmega[n]+PrimePi[FactorInteger[n][[-1,1]]]],{n,100}]
%Y A325134 Cf. A000720, A001222, A052126, A056239, A061395, A093641, A112798, A252464, A257990, A325133, A325135.
%K A325134 nonn
%O A325134 1,2
%A A325134 _Gus Wiseman_, Apr 02 2019