A072965 In prime factorization of n replace all matching twin prime pairs with 1, where (3,5)-matches are replaced before (5,7).

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

Offset: 1

Author

Reinhard Zumkeller, Aug 20 2002

Keywords

• nonn
• nice
• easy

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001359, A006512.

Cf. A027746.

Programs

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

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-François Alcover, Nov 04 2011 *)

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