login
A325225
Lesser of the number of prime factors of n counted with multiplicity and the maximum prime index of n.
16
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.
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.
Sequence in context: A100428 A325169 A322862 * A206719 A240086 A322306
KEYWORD
nonn,hear
AUTHOR
Gus Wiseman, Apr 12 2019
EXTENSIONS
More terms from Antti Karttunen, Apr 14 2019
STATUS
approved