OFFSET
1,7
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.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A366531(n)/2.
EXAMPLE
The prime indices of 198 are {1,2,2,5}, so a(198) = (2+2)/2 = 2.
MAPLE
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:
map(f, [$1..100]); # Robert Israel, Nov 22 2023
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Total[Select[prix[n], EvenQ]]/2, {n, 100}]
CROSSREFS
The triangle for this statistic (without zeros) is A174713.
The un-halved odd version is A366528.
The un-halved version is A366531.
A239261 counts partitions with (sum of odd parts) = (sum of even parts).
A365067 counts partitions by sum of odd parts (without zeros).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2023
STATUS
approved