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A375136
Number of maximal strictly increasing runs in the weakly increasing prime factors of n.
14
0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1
OFFSET
1,4
COMMENTS
For n > 1, this is one more than the number of adjacent equal terms in the multiset of prime factors of n.
FORMULA
For n > 1, a(n) = A046660(n) + 1 = A001222(n) - A001221(n) + 1.
EXAMPLE
The prime factors of 540 are {2,2,3,3,3,5}, with maximal strictly increasing runs ({2},{2,3},{3},{3,5}), so a(540) = 4.
MATHEMATICA
Table[Length[Split[Flatten[ConstantArray@@@FactorInteger[n]], Less]], {n, 100}]
CROSSREFS
For compositions we have A124768, row-lengths of A374683, sum A374684.
For sum of prime indices we have A374706.
Row-lengths of A375128.
A112798 lists prime indices:
- distinct A001221
- length A001222
- leader A055396
- sum A056239
- reverse A296150
Sequence in context: A157754 A072411 A290107 * A212180 A091050 A005361
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 04 2024
STATUS
approved