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A072965
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In prime factorization of n replace all matching twin prime pairs by 1, where (3,5)-matches are replaced before (5,7).
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3
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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; internal format)
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OFFSET
| 1,2
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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 (reinhard.zumkeller(AT)gmail.com), Jan 29 2008
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
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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.
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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}](* From Jean-François Alcover, Nov 04 2011 *)
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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
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CROSSREFS
| Cf. A001359, A006512.
Sequence in context: A080331 A167463 A053835 * A043274 A124196 A139179
Adjacent sequences: A072962 A072963 A072964 * A072966 A072967 A072968
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KEYWORD
| nonn,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2002
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