A099642 a(n) is the smallest nonprime k such that tau(k + n) = tau(k) + n , where tau(n) is the number of divisors of n (A000005).

1, 10, 9, 26, 25, 74, 169, 82, 441, 170, 133, 348, 6889, 166, 3025, 344, 559, 1602, 9981, 820, 9979, 986, 4333, 1236, 9191, 694, 3249, 1652, 3481, 9378, 34969, 3118, 859329, 5636, 36829, 3324, 51947, 3994, 6561, 5000, 15835, 16806, 944741, 6436, 119025

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Example

n=5: a(5)=25 because tau(25)+5 = 3+5 = 8 = tau(25+5) = tau(30).

Mathematica

ds[x_, de_] :=DivisorSigma[0, x+de]-DivisorSigma[0, x]-de; a[n_] :=Block[{m=1, s=ds[m, n]}, While[(s!=0||PrimeQ[m])&&!Greater[m, 10000000], m++ ]; m];

Crossrefs

Cf. A000005, A054905, A305196.

Sequence in context: A309661 A003568 A305196 * A271973 A237114 A217412

Adjacent sequences: A099639 A099640 A099641 * A099643 A099644 A099645

Keyword

nonn

Author

Labos Elemer, Nov 02 2004

Status

approved