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

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

Cf. A000720, A001222, A052126, A056239, A061395, A093641, A112798, A252464, A257990, A325133, A325135.

Sequence in context: A277615 A064066 A297025 * A218007 A060607 A265690

Adjacent sequences: A325131 A325132 A325133 * A325135 A325136 A325137

Keyword

nonn

Author

Gus Wiseman, Apr 02 2019

Status

approved