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Search: id:A160102
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| A160102 |
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Multiplicative function, one-to-one and onto the square-free numbers. |
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+0
1
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| 1, 2, 3, 5, 7, 6, 11, 10, 13, 14, 17, 15, 19, 22, 21, 23, 29, 26, 31, 35, 33, 34, 37, 30, 41, 38, 39, 55, 43, 42, 47, 46, 51, 58, 77, 65, 53, 62, 57, 70, 59, 66, 61, 85, 91, 74, 67, 69, 71, 82, 87, 95, 73, 78, 119, 110, 93, 86, 79, 105, 83, 94, 143, 115, 133, 102, 89, 145
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Multiplicative with a(A050376(k)) = Prime(k) = A000040(k). If k = 2^{i_1} + ... + 2^{i_j} is the binary representation of k, a(p^k) = a(p^2^{i_1}) * ... * a(p^2^{i_j}).
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PROGRAM
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(PARI) al(n)={local(v, k, fm, m, p);
v=vector(n); v[1]=1; p=1;
for(k=2, n, fm=factor(k);
if(matsize(fm)[1]>1, m=fm[1, 1]^fm[1, 2]; v[k]=v[m]*v[k/m],
m=2^valuation(fm[1, 2], 2);
if(m==fm[1, 2], p=nextprime(p+1); v[k]=p,
m=fm[1, 1]^m; v[k]=v[m]*v[k/m])));
v}
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CROSSREFS
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Cf. A005117, A050376, A000040.
Adjacent sequences: A160099 A160100 A160101 this_sequence A160103 A160104 A160105
Sequence in context: A126890 A122637 A076229 this_sequence A137750 A156900 A039734
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KEYWORD
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mult,nonn
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 01 2009
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