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Search: id:A072010
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| A072010 |
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In prime factorization of n replace all primes of form k*4+1 by k*4+3, and primes of form k*4+3 by k*4+1. |
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+0
7
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| 1, 2, 1, 4, 7, 2, 5, 8, 1, 14, 9, 4, 15, 10, 7, 16, 19, 2, 17, 28, 5, 18, 21, 8, 49, 30, 1, 20, 31, 14, 29, 32, 9, 38, 35, 4, 39, 34, 15, 56, 43, 10, 41, 36, 7, 42, 45, 16, 25, 98, 19, 60, 55, 2, 63, 40, 17, 62, 57, 28, 63, 58, 5, 64, 105, 18, 65, 76, 21, 70, 69
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(3^n) = 1; a(2^n) = 2^n;
a(n)>2 is prime iff n=m*3^i (i>=0), a(n)=a(m) and (m,a(m)) or (a(m),m) is a twin prime pair of form ((4*k+1),(4*k+3)), a(m)*m=A071697(j)=A071695(j)*A071696(j) for some j.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Multiplicative with a(p) = p + 2*(2 - p mod 4), p prime.
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EXAMPLE
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a(26928) = a(2^4*3^2*11*17) = a(2)^4 * a(3)^2 * a(11) * a(17)
= 2^4 * 1^2 * 9 * 19 = 2736.
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CROSSREFS
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Cf. A002144, A002145, A072012(n) = a(a(n)).
For a(n) = n see A072011.
Cf. A072014, A072015.
Sequence in context: A091320 A048787 A030102 this_sequence A123360 A072015 A123242
Adjacent sequences: A072007 A072008 A072009 this_sequence A072011 A072012 A072013
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KEYWORD
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nonn,mult,nice
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 05 2002
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