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

3,1

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

Formula

Least k such that A189827(k) = n.

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]

Crossrefs

Cf. A175144.

Sequence in context: A200715 A297901 A079308 * A271878 A259476 A271363

Adjacent sequences: A189822 A189823 A189824 * A189826 A189827 A189828

Keyword

nonn

Author

T. D. Noe, Apr 28 2011

Status

approved