A189825 Least number k such that d(k-1) + d(k+1) = n, where d(k) is the number of divisors of k.

2, 4, 3, 14, 5, 7, 15, 11, 17, 19, 35, 29, 65, 41, 101, 79, 143, 71, 197, 161, 323, 169, 2917, 181, 577, 239, 575, 629, 899, 419, 1297, 701, 901, 721, 25599, 881, 5183, 1121, 9215, 2351, 4901, 1079, 107585, 1681, 36863, 2159, 3601, 2881, 11663, 2519

Offset: 3

Author

T. D. Noe, Apr 28 2011

Keywords

• nonn

Comments

The function d(k-1) + d(k+1) is a measure of the compositeness of the numbers next to k. There is no k for n=1 and n=2. Some terms can be quite large; for example, a(99) = 6533135.

Links

• Donovan Johnson, Table of n, a(n) for n = 3..880

Crossrefs

Cf. A175144.

Programs

Mathematica

nn = 100; t = Table[-1, {nn}]; t[[1]] = t[[2]] = 0; cnt = 2; n = 1; While[cnt < nn, n++; s = DivisorSigma[0,n-1] + DivisorSigma[0,n+1]; If[s <= nn && t[[s]] == -1, t[[s]] = n; cnt++]]; Drop[t,2]

Formula

Least k such that A189827(k) = n.