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A303975
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Number of distinct prime factors in the product of prime indices of n.
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36
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0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 0, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2
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OFFSET
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1,13
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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.
First appearance of n is A062447(n - 1).
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LINKS
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FORMULA
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EXAMPLE
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9193 has prime indices {10, 66} with product 660, which has 4 distinct prime factors {2, 3, 5, 11}, so a(9193) = 4.
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MATHEMATICA
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Table[PrimeNu[If[n==1, 1, Times@@PrimePi/@First/@FactorInteger[n]]], {n, 100}]
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PROG
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(PARI) a(n) = my(v = factor(n)[, 1]); omega(prod(i = 1, #v, primepi(v[i]))) \\ David A. Corneth, Dec 29 2018
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CROSSREFS
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Cf. A000961, A001055, A001221, A002110, A003963, A056239, A112798, A156061, A302242, A302505, A320325.
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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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