

A325224


Sum of prime indices of n minus the lesser of the number of prime factors of n counted with multiplicity and the maximum prime index of n.


8



0, 0, 1, 1, 2, 1, 3, 2, 2, 2, 4, 2, 5, 3, 3, 3, 6, 3, 7, 2, 4, 4, 8, 3, 4, 5, 4, 3, 9, 3, 10, 4, 5, 6, 5, 4, 11, 7, 6, 3, 12, 4, 13, 4, 4, 8, 14, 4, 6, 4, 7, 5, 15, 5, 6, 3, 8, 9, 16, 4, 17, 10, 5, 5, 7, 5, 18, 6, 9, 5, 19, 5, 20, 11, 5, 7, 7, 6, 21, 4, 6, 12
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OFFSET

1,5


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 smaller, 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..82.
FindStat, St000533: The maximal number of nonattacking rooks on a Ferrers shape


FORMULA

a(n) = A056239(n)  min(A001222(n), A061395(n)) = A056239(n)  A325225(n).


EXAMPLE

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


MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 0, Total[primeMS[n]]Min[Length[primeMS[n]], Max[primeMS[n]]]], {n, 100}]


CROSSREFS

The number of times k appears in the sequence is A325232(k).
Cf. A001222, A052126, A056239, A061395, A064989, A065770, A112798, A174090, A257990, A263297, A325134, A325169, A325223, A325225, A325227.
Sequence in context: A035221 A035191 A297167 * A303389 A276166 A177062
Adjacent sequences: A325221 A325222 A325223 * A325225 A325226 A325227


KEYWORD

nonn


AUTHOR

Gus Wiseman, Apr 12 2019


STATUS

approved



