OFFSET
1,2
COMMENTS
We define the skew-alternating sum of a sequence (A, B, C, D, E, F, G, ...) to be A - B - C + D + E - F - G + ....
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.
EXAMPLE
The terms together with their prime indices begin:
1: {}
4: {1,1}
9: {2,2}
16: {1,1,1,1}
25: {3,3}
36: {1,1,2,2}
49: {4,4}
64: {1,1,1,1,1,1}
81: {2,2,2,2}
90: {1,2,2,3}
100: {1,1,3,3}
121: {5,5}
144: {1,1,1,1,2,2}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
skats[f_]:=Sum[f[[i]]*(-1)^(1+Ceiling[(i+1)/2]), {i, Length[f]}];
Select[Range[1000], skats[primeMS[#]]==0&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 09 2022
STATUS
approved