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A366533
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Sum of even prime indices of n divided by 2.
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15
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0, 0, 1, 0, 0, 1, 2, 0, 2, 0, 0, 1, 3, 2, 1, 0, 0, 2, 4, 0, 3, 0, 0, 1, 0, 3, 3, 2, 5, 1, 0, 0, 1, 0, 2, 2, 6, 4, 4, 0, 0, 3, 7, 0, 2, 0, 0, 1, 4, 0, 1, 3, 8, 3, 0, 2, 5, 5, 0, 1, 9, 0, 4, 0, 3, 1, 0, 0, 1, 2, 10, 2, 0, 6, 1, 4, 2, 4, 11, 0, 4, 0, 0, 3, 0, 7
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OFFSET
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1,7
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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The prime indices of 198 are {1,2,2,5}, so a(198) = (2+2)/2 = 2.
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MAPLE
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f:= proc(n) local F, t;
F:= map(t -> [numtheory:-Pi(t[1]), t[2]], ifactors(n)[2]);
add(`if`(t[1]::even, t[1]*t[2]/2, 0), t=F)
end proc:
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Total[Select[prix[n], EvenQ]]/2, {n, 100}]
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CROSSREFS
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The triangle for this statistic (without zeros) is A174713.
The un-halved odd version is A366528.
A066207 lists numbers with all even prime indices, counted by A035363.
A239261 counts partitions with (sum of odd parts) = (sum of even parts).
A365067 counts partitions by sum of odd parts (without zeros).
A366322 lists numbers with not all prime indices even, counted by A086543.
Cf. A000720, A055396, A055922, A061395, A162641, A171966, A258117, A325698, A325700, A352140, A352141.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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