A340691 - OEIS

A340691

Greatest image of A001222 over the prime indices of n.

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

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OFFSET

1,7

COMMENTS

For the initial term, we assume the empty set has maximum image 0.

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

Table of n, a(n) for n=1..88.

EXAMPLE

The prime indices of 4070 are {1,3,5,12} -> {0,1,1,3}, so a(4070) = 3.

The prime indices of 8892 are {1,1,2,2,6,8} -> {0,0,1,1,2,3} so a(8892) = 3.

MATHEMATICA

Table[If[n==1, 0, Max@@PrimeOmega/@PrimePi/@First/@FactorInteger[n]], {n, 100}]

CROSSREFS

Positions of first appearances are A033844.

Positions of 0's are A000079.

Positions of terms <= 1 are A302540.

Positions of 1's are A302540 \ A000079.

The version for minimum is A340928.

A003963 multiplies together the prime indices.

A056239 adds up the prime indices.

A061395 selects the greatest prime index.

A072233 counts partitions by sum and maximum.

A112798 lists the prime indices of each positive integer.

A303975 counts distinct prime factors in the product of prime indices.

Cf. A001222, A006530, A062447, A106529, A244990, A244991, A324522, A340606, A340609, A340610, A340856.

Sequence in context: A050332 A369258 A337930 * A216658 A214020 A029425

Adjacent sequences: A340688 A340689 A340690 * A340692 A340693 A340694

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 28 2021

STATUS

approved