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Search: id:A076931
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| A076931 |
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Smallest k such that n*k has n divisors. |
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+0
4
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| 1, 1, 3, 2, 125, 2, 16807, 3, 4, 8, 2357947691, 5, 1792160394037, 32, 135, 24, 2862423051509815793, 10, 5480386857784802185939, 12, 1701, 512, 39471584120695485887249589623, 15, 400, 2048, 972, 48, 3053134545970524535745336759489912159909
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OFFSET
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1,3
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COMMENT
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n=p_1^a_1*...*p_r^a_r => tau(p_1^(p_1^a_1-1)*...*p_r^(p_r^a_r-1))=n, so sequence is well-defined.
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FORMULA
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a(p)=p^(p-2), a(pq)=p^(q-2)*q^(p-2) for p<q, a(2^2)=2, a(p^2)=p^(p-3)*2^(p-1) for p!=2.
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MATHEMATICA
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f[n_] := Block[{k = 1, m = If[ PrimeQ[n], n^(n-2), 1]}, While[ DivisorSigma[0, k*m*n] != n, k++ ]; k*m]; Table[f[n], {n, 29}] from Robert G. Wilson v (rgwv(at)rgwv.com), Sep 29 2005
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CROSSREFS
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a(n)= A073904(n)/n.
Sequence in context: A069576 A109899 A002297 this_sequence A076932 A065585 A139737
Adjacent sequences: A076928 A076929 A076930 this_sequence A076932 A076933 A076934
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 18 2002
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EXTENSIONS
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More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Jan 21 2003
More terms from David Wasserman (dwasserm(AT)earthlink.net), Aug 19 2005
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