A325134 - OEIS

A325134

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

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, 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, 13, 7, 7, 8, 8, 20, 10, 11, 7, 21, 7, 22, 14, 6, 11, 7, 9, 23

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OFFSET

1,2

COMMENTS

A prime index of n is a number m such that prime(m) divides n.

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).

LINKS

Table of n, a(n) for n=1..79.

FORMULA

a(n) = A001222(n) + A061395(n).

a(n) = A252464(n) + 1.

MAPLE

with(numtheory):

a:= n-> `if`(n=1, 1, bigomega(n)+pi(max(factorset(n)[]))):

seq(a(n), n=1..100); # Alois P. Heinz, Apr 03 2019

MATHEMATICA

Table[If[n==1, 1, PrimeOmega[n]+PrimePi[FactorInteger[n][[-1, 1]]]], {n, 100}]

CROSSREFS