OFFSET
2,2
COMMENTS
Row 1 is empty, so offset is 2.
The first sums of a sequence (a, b, c, d, ...) are (a+b, b+c, c+d, ...).
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.
There are no duplicate rows.
EXAMPLE
The prime indices of 9 are (2,2), 1-prepended (1,2,2), first sums (3,4), minus 1 (2,3), so row 9 is (2,3).
The prime indices of 12 are (1,1,2), 1-prepended (1,1,1,2), first sums (2,2,3), minus 1 (1,1,2), so row 12 is also (1,1,2).
Triangle begins:
1:
2: 1
3: 2
4: 1 1
5: 3
6: 1 2
7: 4
8: 1 1 1
9: 2 3
10: 1 3
11: 5
12: 1 1 2
13: 6
14: 1 4
15: 2 4
16: 1 1 1 1
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
firsums[c_]:=Table[c[[i]]+c[[i+1]], {i, Length[c]-1}];
Table[firsums[Prepend[prix[n], 1]]-1, {n, 100}]
CROSSREFS
Positions of singleton rows are A000040.
Row-lengths are A001222.
The first term of each row is A055396.
Positions of constant rows are A174090.
The non-prepended version is A325389.
A243056 gives maximum prime index minus minimum prime index.
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 05 2025
STATUS
approved