OFFSET
1,9
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10201
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
FORMULA
EXAMPLE
The partition with Heinz number 1100 is (5,3,3,1,1), so a(1100) = 3 + 1 = 4.
The partition with Heinz number 2100 is (4,3,3,2,1,1), so a(2100) = 3 + 2 + 1 = 6.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Total[Last/@Partition[Reverse[primeMS[n]], 2]], {n, 100}]
PROG
(PARI) A346700(n) = if(1==n, 0, my(f=factor(n), s=0, p=0); forstep(k=#f~, 1, -1, while(f[k, 2], s += (p%2)*primepi(f[k, 1]); f[k, 2]--; p++)); (s)); \\ Antti Karttunen, Sep 21 2021
CROSSREFS
Sum of prime indices of A329888(n).
The unreversed version for standard compositions is A346633.
The odd non-reverse version is A346697.
The non-reverse version (multisets instead of partitions) is A346698.
The odd version is A346699.
A344606 counts alternating permutations of prime indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 03 2021
EXTENSIONS
Data section extended up to 105 terms by Antti Karttunen, Sep 21 2021
STATUS
approved