A076931 Smallest k such that n*k has n divisors.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..29.

Formula

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.

Mathematica

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}] (* Robert G. Wilson v, Sep 29 2005 *)

Crossrefs

a(n)= A073904(n)/n.

Sequence in context: A002297 A183270 A152017 * A076932 A244083 A303683

Adjacent sequences: A076928 A076929 A076930 * A076932 A076933 A076934

Keyword

nonn

Author

Amarnath Murthy, Oct 18 2002

Extensions

More terms from Sascha Kurz, Jan 21 2003

More terms from David Wasserman, Aug 19 2005

Status

approved