OFFSET
1,2
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.
The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(k-i) y_i.
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are also Heinz numbers of partitions whose sum is twice their reverse-alternating sum.
EXAMPLE
The terms and their prime indices begin:
1: ()
10: (3,1)
12: (2,1,1)
39: (6,2)
63: (4,2,2)
66: (5,2,1)
88: (5,1,1,1)
112: (4,1,1,1,1)
115: (9,3)
190: (8,3,1)
228: (8,2,1,1)
255: (7,3,2)
259: (12,4)
306: (7,2,2,1)
325: (6,3,3)
408: (7,2,1,1,1)
434: (11,4,1)
468: (6,2,2,1,1)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
sats[y_]:=Sum[(-1)^(i-Length[y])*y[[i]], {i, Length[y]}];
Select[Range[1000], Total[primeMS[#]]==2*sats[primeMS[#]]&]
CROSSREFS
These partitions are counted by A006330 up to 0's.
The negative reverse version is A348617.
The non-reverse version is A349159.
A346697 adds up odd-indexed prime indices.
A346698 adds up even-indexed prime indices.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2021
STATUS
approved