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A072965 In prime factorization of n replace all matching twin prime pairs with 1, where (3,5)-matches are replaced before (5,7). 3
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2, 31, 32, 33, 34, 1, 36, 37, 38, 39, 40, 41, 42, 43, 44, 3, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 4, 61, 62, 63, 64, 65, 66, 67, 68, 69, 2, 71, 72, 73, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(a(n)) = a(n); a(A037074(n)) = 1.

a(n) = 1 iff n = A074480(k) for some k.

a(n) mod A037074(k) > 0 for all k. - Reinhard Zumkeller, Jan 29 2008

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

a(30)=a(2*3*5)=2*1=2; a(105)=a(3*5*7)=1*7=7; a(143)=a(11*13)=1; a(225)=a(3*3*5*5)=a(3*5)*(3*5))=1*1=1; a(525)=a(3*5*5*7)=a((3*5)*(5*7))=1*1=1.

MATHEMATICA

a[n_] := Times @@ (Flatten[ (Table[#[[1]], {#[[2]]}] & ) /@ FactorInteger[n]] //. {p1___, p2_, p3_, p4___} /; p3 == p2 + 2 -> {p1, p4}); Table[a[n], {n, 1, 74}](* Jean-Fran├žois Alcover, Nov 04 2011 *)

PROG

(PARI) a(n)=my(f=factor(n), t); for(i=2, #f[, 1], if(f[i-1, 1]+2==f[i, 1], t=min(f[i-1, 2], f[i, 2]); f[i-1, 2]-=t; f[i, 2]-=t)); factorback(f) \\ Charles R Greathouse IV, Nov 04 2011

(Haskell)

a072965 n = f 1 (a027746_row n) where

   f y []      = y

   f y [p]     = p * y

   f y (2:ps)  = f (2 * y) ps

   f y (3:5:_) = a072965 (n `div` 15)

   f y (p:qs@(q:ps)) | q == p + 2 = f y ps

                     | otherwise  = f (p * y) qs

-- Reinhard Zumkeller, Oct 31 2012

CROSSREFS

Cf. A001359, A006512.

Cf. A027746.

Sequence in context: A297247 A167463 A053835 * A297248 A043274 A318891

Adjacent sequences:  A072962 A072963 A072964 * A072966 A072967 A072968

KEYWORD

nonn,nice

AUTHOR

Reinhard Zumkeller, Aug 20 2002

STATUS

approved

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Last modified August 12 21:10 EDT 2020. Contains 336440 sequences. (Running on oeis4.)