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A102048
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Exponent of A046021(n) (least inverse of Kempner-Smarandache function A002034) when written as a power of A006530(n) (largest prime dividing n), with a(1) = 1.
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1
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1, 1, 1, 2, 1, 2, 1, 5, 3, 2, 1, 5, 1, 2, 3, 12, 1, 7, 1, 4, 3, 2, 1, 10, 5, 2, 11, 4, 1, 7, 1, 27, 3, 2, 5, 16, 1, 2, 3, 9, 1, 6, 1, 4, 10, 2, 1, 22, 7, 11, 3, 4, 1, 24, 5, 9, 3, 2, 1, 14, 1, 2, 10, 58, 5, 6, 1, 4, 3, 11, 1, 33, 1, 2, 17, 4, 7, 6, 1, 19, 37, 2, 1, 13, 5, 2, 3, 8, 1, 21, 7, 4, 3, 2, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) = log(A046021(n))/log(A006530(n)) for n>1.
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REFERENCES
| R. L. Graham, D. E. Knuth and O. Patashnik, Factorial Factors, Section 4.4 in Concrete Mathematics, 2nd ed. Reading, MA: Addison-Wesley, pp. 111-115, 1994.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to factorial numbers.
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FORMULA
| 1+Sum(k=1 to [log(n-1)/log(P)], [(n-1)/P^k]) for n>1, where P = A006530(n) is the greatest prime factor of n.
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EXAMPLE
| a(6) = 2 because A046021(6) = 9 = 3^2 = A006530(6)^2.
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MATHEMATICA
| With[{p=First[Last[FactorInteger[n, FactorComplete->True]]]}, 1+Sum[Floor[(n-1)/p^k], {k, Floor[Log[n-1]/Log[p]]}]]
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CROSSREFS
| Cf. A046021, A006530.
Sequence in context: A172133 A146002 A109087 * A102551 A152823 A086545
Adjacent sequences: A102045 A102046 A102047 * A102049 A102050 A102051
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KEYWORD
| nonn
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AUTHOR
| Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 26 2004
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