OFFSET
0,2
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 weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.
EXAMPLE
The terms together with their prime indices begin:
1: {}
2: {1}
3: {2}
5: {3}
7: {4}
11: {5}
14: {1,4}
22: {1,5}
26: {1,6}
34: {1,7}
44: {1,1,5}
55: {3,5}
68: {1,1,7}
85: {3,7}
110: {1,3,5}
130: {1,3,6}
170: {1,3,7}
190: {1,3,8}
242: {1,5,5}
290: {1,3,10}
The 6 numbers with weighted sum of reversed prime indices 9, together with their prime indices:
18: {1,2,2}
23: {9}
25: {3,3}
28: {1,1,4}
33: {2,5}
34: {1,7}
Hence a(9) = 34.
MATHEMATICA
nn=10;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
ots[y_]:=Sum[i*y[[i]], {i, Length[y]}];
seq=Table[ots[Reverse[primeMS[n]]], {n, 1, 2^nn}];
Table[Position[seq, k][[-1, 1]], {k, 0, nn}]
CROSSREFS
The unreversed version is A359497.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2023
EXTENSIONS
More terms from Jinyuan Wang, Jan 26 2023
STATUS
approved