|
|
A355536
|
|
Irregular triangle read by rows where row n lists the differences between adjacent prime indices of n; if n is prime, row n is empty.
|
|
34
|
|
|
0, 1, 0, 0, 0, 2, 0, 1, 3, 1, 0, 0, 0, 1, 0, 0, 2, 2, 4, 0, 0, 1, 0, 5, 0, 0, 0, 3, 1, 1, 0, 0, 0, 0, 3, 6, 1, 0, 1, 0, 7, 4, 0, 0, 2, 1, 2, 0, 4, 0, 1, 8, 0, 0, 0, 1, 0, 2, 0, 5, 0, 5, 1, 0, 0, 2, 0, 0, 3, 6, 9, 0, 1, 1, 10, 0, 2, 0, 0, 0, 0, 0, 3, 1, 3, 0, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,6
|
|
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 version where zero is prepended to the prime indices is A287352.
One could argue that row n = 1 is empty, but adding it changes only the offset, not the data.
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins (showing n, prime indices, differences*):
2: (1) .
3: (2) .
4: (1,1) 0
5: (3) .
6: (1,2) 1
7: (4) .
8: (1,1,1) 0 0
9: (2,2) 0
10: (1,3) 2
11: (5) .
12: (1,1,2) 0 1
13: (6) .
14: (1,4) 3
15: (2,3) 1
16: (1,1,1,1) 0 0 0
|
|
MATHEMATICA
|
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Differences[primeMS[n]], {n, 2, 100}]
|
|
CROSSREFS
|
Constant rows have indices A325328.
The Heinz numbers of the rows plus one are A325352.
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|