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A357458
First differences of A325033 = "Sum of sums of the multiset of prime indices of each prime index of n."
1
0, 1, -1, 2, -1, 1, -2, 2, 0, 1, -2, 2, -1, 1, -3, 4, -2, 1, -1, 1, 0, 1, -3, 3, -1, 0, -1, 2, -1, 2, -5, 4, 0, 0, -2, 2, -1, 1, -2, 4, -3, 2, -2, 1, 0, 1, -4, 3, 0, 1, -2, 1, -1, 2, -3, 2, 0, 3, -4, 2, 0, -1, -4, 5, -1, 4, -4, 1, -1, 1, -3, 4, -2, 1, -2, 2
OFFSET
1,4
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 multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
FORMULA
a(n) = A325033(n + 1) - A325033(n).
EXAMPLE
We have A325033(5) - A325033(4) = 2 - 0, so a(4) = 2.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Differences[Table[Plus@@Join@@primeMS/@primeMS[n], {n, 100}]]
CROSSREFS
The partial sums are A325033, which has row-products A325032.
The version for standard compositions is A357187.
A000961 lists prime powers.
A003963 multiples prime indices.
A005117 lists squarefree numbers.
A056239 adds up prime indices.
Sequence in context: A355912 A034798 A225803 * A349277 A307014 A240871
KEYWORD
sign
AUTHOR
Gus Wiseman, Sep 30 2022
STATUS
approved