A325225 Lesser of the number of prime factors of n counted with multiplicity and the maximum prime index of n.

0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 3, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 2, 3, 1, 2, 2, 4, 2, 2, 1, 3, 1, 2, 3, 1, 2, 3, 1, 3, 2, 3, 1, 2, 1, 2, 3, 3, 2, 3, 1, 3, 2, 2, 1, 4, 2, 2, 2, 4, 1, 3, 2, 3, 2, 2, 2, 2, 1, 3, 3, 3, 1, 3, 1, 4, 3

Offset: 1

Author

Gus Wiseman, Apr 12 2019

Keywords

• nonn
• hear

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			88 has 4 prime indices {1,1,1,5}, the maximum of which is 5, so a(88) = min(4,5) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• FindStat, St000533: The maximal number of non-attacking rooks on a Ferrers shape

Crossrefs

Positions of 1's are A174090. Positions of 2's are A325229.

Cf. A001222, A056239, A061395, A065770, A093641, A112798, A252464, A257541, A257990, A263297, A325169, A325224, A325227, A325232.

Programs

Mathematica

Table[Min[PrimeOmega[n],PrimePi[FactorInteger[n][[-1,1]]]],{n,100}]

PARI

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A325225(n) = min(bigomega(n), A061395(n)); \\ Antti Karttunen, Apr 14 2019

Formula

a(n) = min(A001222(n), A061395(n)).

Extensions

More terms from Antti Karttunen, Apr 14 2019