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A370820
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Number of positive integers that are a divisor of some prime index of n.
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26
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0, 1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 4, 3, 3, 1, 2, 2, 4, 2, 3, 2, 3, 2, 2, 4, 2, 3, 4, 3, 2, 1, 3, 2, 4, 2, 6, 4, 4, 2, 2, 3, 4, 2, 3, 3, 4, 2, 3, 2, 3, 4, 5, 2, 3, 3, 4, 4, 2, 3, 6, 2, 3, 1, 4, 3, 2, 2, 4, 4, 6, 2, 4, 6, 3, 4, 4, 4, 4, 2, 2, 2, 2, 3, 3, 4, 4
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OFFSET
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1,3
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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.
This sequence contains all nonnegative integers. In particular, a(prime(n)!) = n.
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LINKS
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EXAMPLE
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2045 has prime indices {3,80} with combined divisors {1,2,3,4,5,8,10,16,20,40,80}, so a(2045) = 11. In fact, 2045 is the least number with this property.
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MATHEMATICA
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Table[Length[Union@@Divisors/@PrimePi/@First/@If[n==1, {}, FactorInteger[n]]], {n, 100}]
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PROG
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(PARI) a(n) = my(list=List(), f=factor(n)); for (i=1, #f~, fordiv(primepi(f[i, 1]), d, listput(list, d))); #Set(list); \\ Michel Marcus, May 02 2024
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CROSSREFS
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Positions of ones are A000079 except for 1.
a(prime(n)!) = a(prime(A005179(n))) = n.
Counting prime factors instead of divisors gives A303975.
Position of first appearance of n is A371131(n), sorted version A371181.
A001221 counts distinct prime factors.
A003963 gives product of prime indices.
A355731 counts choices of a divisor of each prime index, firsts A355732.
A355741 counts choices of a prime factor of each prime index.
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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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