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A325223 Sum of the prime indices of n minus the greater of the number of prime factors of n counted with multiplicity and the largest prime index of n. 3
0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 1, 0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 0, 1, 3, 1, 3, 2, 0, 3, 0, 0, 2, 1, 3, 2, 0, 1, 2, 2, 0, 3, 0, 2, 4, 1, 0, 1, 4, 4, 2, 2, 0, 3, 3, 3, 2, 1, 0, 3, 0, 1, 4, 0, 3, 3, 0, 2, 2, 4, 0, 2, 0, 1, 5, 2, 4, 3, 0, 2, 4, 1, 0, 4, 3, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

A prime index of n is a number m such that prime(m) divides n.

Also the number of squares in the Young diagram of the integer partition with Heinz number n after the first row or the first column, whichever is larger, is removed. 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..87.

FindStat, St000784: The maximum of the length and the largest part of the integer partition

FORMULA

a(n) = A056239(n) - max(A001222(n), A061395(n)) = A056239(n) - A263297(n).

EXAMPLE

88 has 4 prime indices {1,1,1,5} with sum 8 and maximum 5, so a(88) = 8 - max(4,5) = 3.

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Table[Total[primeMS[n]]-Max[Length[primeMS[n]], Max[primeMS[n]]], {n, 100}]

CROSSREFS

Positions of 0's are A174090. Positions of 1's are A325231.

Cf. A001222, A051924, A052126, A056239, A061395, A064989, A065770, A112798, A257990, A263297, A325134, A325169, A325224, A325225, A325227.

Sequence in context: A092111 A307776 A050317 * A141095 A175599 A179759

Adjacent sequences:  A325220 A325221 A325222 * A325224 A325225 A325226

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 12 2019

STATUS

approved

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Last modified June 24 13:17 EDT 2019. Contains 324325 sequences. (Running on oeis4.)