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 A117364 a(n) = largest prime less than the largest prime dividing n (or 1 if there is no such prime). 3
 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; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS EXAMPLE 5 is the largest prime dividing 10. So a(10) is the largest prime < 5, which is 3. MATHEMATICA 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 *) CROSSREFS Cf. A117365, A117366, A117367. Sequence in context: A024467 A215489 A182167 * A193615 A300383 A120250 Adjacent sequences:  A117361 A117362 A117363 * A117365 A117366 A117367 KEYWORD nonn AUTHOR Leroy Quet, Mar 10 2006 EXTENSIONS More terms from Robert G. Wilson v, May 01 2006 STATUS approved

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Last modified September 21 21:32 EDT 2021. Contains 347605 sequences. (Running on oeis4.)