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 A014673 Smallest prime factor of greatest proper divisor of n. 17
 1, 1, 1, 2, 1, 3, 1, 2, 3, 5, 1, 2, 1, 7, 5, 2, 1, 3, 1, 2, 7, 11, 1, 2, 5, 13, 3, 2, 1, 3, 1, 2, 11, 17, 7, 2, 1, 19, 13, 2, 1, 3, 1, 2, 3, 23, 1, 2, 7, 5, 17, 2, 1, 3, 11, 2, 19, 29, 1, 2, 1, 31, 3, 2, 13, 3, 1, 2, 23, 5, 1, 2, 1, 37, 5, 2, 11, 3, 1, 2, 3, 41, 1, 2, 17, 43, 29, 2, 1, 3, 13, 2, 31, 47 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS For n > 1: a(n) = 1 iff n is prime; a(A001358(n)) = A084127(n); a(A025475(n)) = A020639(A025475(n)). [corrected by Peter Munn, Feb 19 2017] When n is composite, this is the 2nd factor when n is written as a product of primes in nondecreasing order. For example, 12 = 2*2*3, so a(12) = 2. - Peter Munn, Feb 19 2017 For all sufficiently large n the median value of a(1), a(2), ... a(n) is A281889(2) = 7. - Peter Munn, Jul 12 2019 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A020639(A032742(n)). A117357(n) = A020639(A054576(n)); A117358(n) = A032742(A054576(n)) = A054576(n)/A117357(n). - Reinhard Zumkeller, Mar 10 2006 If A001222(n) >= 2, a(n) = A027746(n,2), otherwise a(n) = 1. - Peter Munn, Jul 13 2019 MATHEMATICA PrimeFactors[ n_ ] := Flatten[ Table[ # [ [ 1 ] ], {1} ] & /@ FactorInteger[ n ] ]; f[ n_ ] := Block[ {gpd = Divisors[ n ][ [ -2 ] ]}, If[ gpd == 1, 1, PrimeFactors[ gpd ][ [ 1 ] ] ] ]; Table[ If[ n == 1, 1, f[ n ] ], {n, 1, 95} ] (* Second program: *) Table[If[Or[PrimeQ@ n, n == 1], 1, FactorInteger[n/SelectFirst[Prime@ Range@ PrimePi[Sqrt@ n], Divisible[n, #] &]][[1, 1]] ], {n, 94}] (* Michael De Vlieger, Aug 14 2017 *) PROG (PARI) lpf(n)=if(n>1, factor(n)[1, 1], 1) a(n)=lpf(n/lpf(n)) \\ Charles R Greathouse IV, May 09 2013 (PARI) a(n)=if(n<4||isprime(n), return(1)); my(f=factor(n)); if(f[1, 2]>1, f[1, 1], f[2, 1]) \\ Charles R Greathouse IV, May 09 2013 (Scheme) (define (A014673 n) (A020639 (/ n (A020639 n)))) ;; Code for A020639 given under that entry - Antti Karttunen, Aug 12 2017 CROSSREFS Cf. A001222, A001358, A020639, A025475, A027746, A032742, A054576, A084127, A085392, A085393, A115561, A117357, A117358, A281889. Sequence in context: A329585 A128487 A056609 * A346704 A280686 A085392 Adjacent sequences: A014670 A014671 A014672 * A014674 A014675 A014676 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jun 24 2003 STATUS approved

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Last modified December 7 08:27 EST 2023. Contains 367645 sequences. (Running on oeis4.)