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

1,6

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.

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

Formula

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

Example

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

Mathematica

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

Prog

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

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.

Sequence in context: A100428 A325169 A322862 * A206719 A240086 A322306

Adjacent sequences: A325222 A325223 A325224 * A325226 A325227 A325228

Keyword

nonn,hear

Author

Gus Wiseman, Apr 12 2019

Extensions

More terms from Antti Karttunen, Apr 14 2019

Status

approved