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 A357139 Take the weakly increasing prime indices of each prime index of n, then concatenate. 4
 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 5, 1, 3, 4, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 6, 1, 1, 1, 1, 4, 3, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 2, 2, 1, 4, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. LINKS Table of n, a(n) for n=1..87. EXAMPLE Triangle begins: 1: 2: 3: 1 4: 5: 2 6: 1 7: 1 1 8: 9: 1 1 10: 2 11: 3 12: 1 13: 1 2 For example, the weakly increasing prime indices of 105 are (2,3,4), with prime indices ((1),(2),(1,1)), so row 105 is (1,2,1,1). MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Join@@Table[Join@@primeMS/@primeMS[n], {n, 100}] CROSSREFS Row lengths are A302242. Positions of strict rows are A302505. Positions of constant rows are A302593. Row sums are A325033, products A325032. The version for standard compositions is A357135, rank A357134. A000961 lists prime powers. A003963 multiples prime indices. A056239 adds up prime indices. Cf. A000720, A001221, A001222, A007716, A058891, A109082, A275024, A302243, A324926, A325034. Sequence in context: A326753 A062093 A177457 * A046214 A232088 A115413 Adjacent sequences: A357136 A357137 A357138 * A357140 A357141 A357142 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Sep 29 2022 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)