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A014673 Smallest prime factor of greatest proper divisor of n. 14
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

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

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. A085392, A085393.

Sequence in context: A096107 A128487 A056609 * A280686 A085392 A089384

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 13 09:55 EST 2017. Contains 295957 sequences.