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A338913
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Greater prime index of the n-th semiprime.
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44
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1, 2, 2, 3, 4, 3, 4, 5, 3, 6, 5, 7, 4, 8, 6, 9, 4, 7, 5, 8, 10, 11, 6, 9, 12, 5, 13, 7, 14, 10, 6, 11, 15, 8, 16, 12, 9, 17, 7, 5, 18, 13, 14, 8, 19, 15, 20, 6, 10, 21, 11, 22, 16, 9, 23, 6, 17, 24, 18, 12, 7, 25, 19, 26, 10, 13, 27, 8, 20, 28, 14, 11, 29, 21
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OFFSET
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1,2
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COMMENTS
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A semiprime is a product of any two prime numbers. 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.
After the first three terms, there appear to be no adjacent equal terms.
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LINKS
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FORMULA
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EXAMPLE
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The semiprimes are:
2*2, 2*3, 3*3, 2*5, 2*7, 3*5, 3*7, 2*11, 5*5, 2*13, ...
so the greater prime factors are:
2, 3, 3, 5, 7, 5, 7, 11, 5, 13, ...
with indices:
1, 2, 2, 3, 4, 3, 4, 5, 3, 6, ...
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MATHEMATICA
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Table[Max[PrimePi/@First/@FactorInteger[n]], {n, Select[Range[100], PrimeOmega[#]==2&]}]
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CROSSREFS
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A115392 lists positions of first appearances of each positive integer.
A338912 is the corresponding lesser prime index.
A001221 counts distinct prime indices.
Cf. A037143, A056239, A065516, A084126, A084127, A112798, A128301, A289182, A320732, A320892, A338900, A338904, A338909.
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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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