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A355526
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Maximal difference between adjacent prime indices of n, or k if n is the k-th prime.
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12
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1, 2, 0, 3, 1, 4, 0, 0, 2, 5, 1, 6, 3, 1, 0, 7, 1, 8, 2, 2, 4, 9, 1, 0, 5, 0, 3, 10, 1, 11, 0, 3, 6, 1, 1, 12, 7, 4, 2, 13, 2, 14, 4, 1, 8, 15, 1, 0, 2, 5, 5, 16, 1, 2, 3, 6, 9, 17, 1, 18, 10, 2, 0, 3, 3, 19, 6, 7, 2, 20, 1, 21, 11, 1, 7, 1, 4, 22, 2, 0, 12
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OFFSET
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2,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The prime indices of 9842 are {1,4,8,12}, with differences (3,4,4), so a(9842) = 4.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[PrimeQ[n], PrimePi[n], Max@@Differences[primeMS[n]]], {n, 2, 100}]
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CROSSREFS
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Crossrefs found in the link are not repeated here.
Positions of first appearances are 4 followed by A000040.
Prepending 0 to the prime indices gives A286469, minimal version A355528.
A001522 counts partitions with a fixed point (unproved), ranked by A352827.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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