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
Keywords
Examples
n=5: a(5)=25 because tau(25)+5 = 3+5 = 8 = tau(25+5) = tau(30).
Programs
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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];