A190612 Numbers k such that (tau(k-1) + tau(k+1))/tau(k) is an integer, where tau(k)=A000005(k).

6, 7, 11, 13, 19, 20, 23, 25, 28, 29, 31, 32, 34, 39, 41, 43, 46, 47, 51, 52, 53, 55, 56, 57, 59, 61, 62, 67, 68, 71, 73, 74, 79, 83, 85, 86, 87, 89, 94, 95, 97, 103, 107, 109, 113, 119, 127, 129, 131, 133, 134, 137, 139, 141, 142, 149, 151, 152, 155, 157

Offset: 1

Author

Juri-Stepan Gerasimov, May 14 2011

Keywords

• nonn

Examples

			6 is a term because (tau(5) + tau(7))/tau(6) = 1;
7 is a term because (tau(6) + tau(8))/tau(7) = 4;
11 is a term because (tau(10) + tau(12))/tau(11) = 5;
13 is a term because (tau(12) + tau(14))/tau(13) = 5.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of a(n)/n for n = 1..2000000

Crossrefs

Cf. A000005 (number of divisors of n), A074757, A090502.

Programs

Maple

with(numtheory): A190612 := proc(n) option remember: local k: if(n=1)then return 6:fi: for k from procname(n-1)+1 do if(tau(k-1)+tau(k+1) mod tau(k) = 0)then return k: fi: od: end: seq(A190612(n),n=1..70); # Nathaniel Johnston, May 14 2011

Mathematica

Select[Range[200], IntegerQ[(DivisorSigma[0, #-1] + DivisorSigma[0, #+1]) / DivisorSigma[0, #]] &] (* Vaclav Kotesovec, Feb 14 2019 *)