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Search: id:A117364
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| A117364 |
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a(n) = largest prime less than the largest prime dividing n (or 1 if there is no such prime). |
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4
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| 1, 1, 2, 1, 3, 2, 5, 1, 2, 3, 7, 2, 11, 5, 3, 1, 13, 2, 17, 3, 5, 7, 19, 2, 3, 11, 2, 5, 23, 3, 29, 1, 7, 13, 5, 2, 31, 17, 11, 3, 37, 5, 41, 7, 3, 19, 43, 2, 5, 3, 13, 11, 47, 2, 7, 5, 17, 23, 53, 3, 59, 29, 5, 1, 11, 7, 61, 13, 19, 5, 67, 2, 71, 31, 3, 17, 7, 11, 73, 3, 2, 37, 79, 5, 13, 41, 23
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = 1 if and only if n is a power of 2 (including 1).
a(n/3) = 2 iff n/3 is A003586: 3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.
a(n/5) = 3 iff n/5 is A051037: 5-smooth numbers: i.e. numbers whose prime divisors are all <= 5, etc.
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EXAMPLE
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5 is the largest prime dividing 10. So a(10) is the largest prime < 5, which is 3.
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MATHEMATICA
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PrevPrime[n_] := Block[{k = n - 1}, While[ ! PrimeQ[k], k-- ]; k]; f[n_] := Block[{k = PrevPrime@ FactorInteger[Max[2, n]][[ -1, 1]]}, If[k > 1, k, 1]]; Array[f, 87] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A117365, A117366, A117367.
Sequence in context: A022447 A117194 A024467 this_sequence A120250 A116529 A064989
Adjacent sequences: A117361 A117362 A117363 this_sequence A117365 A117366 A117367
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Mar 10 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), May 01 2006
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