A036434 Integers which cannot be written as k+tau(k) for some k.

1, 3, 6, 8, 11, 16, 17, 20, 22, 23, 27, 29, 35, 36, 40, 41, 44, 46, 47, 53, 54, 57, 60, 65, 67, 68, 70, 76, 77, 79, 80, 83, 87, 88, 92, 93, 94, 100, 101, 106, 107, 114, 116, 117, 121, 125, 128, 131, 132, 134, 135, 140, 142, 148, 155, 156, 157, 158, 161, 164, 166

Offset: 1

Author

Simon Colton (simonco(AT)cs.york.ac.uk)

Keywords

• nonn

Comments

Invented by the HR concept formation program.

Indices of 0's in A036431. - Sean A. Irvine, Nov 01 2020

Examples

			None of 1,2,3,4,5,6,7 are such that k+tau(k)=8, so 8 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Simon Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2 (1999), Article 99.1.2.
• Simon Colton, HR - Automatic Theory Formation in Pure Mathematics.

Crossrefs

Cf. A036431, A036438, A062249.

Programs

Mathematica

m = 200; Complement[Range[m], Table[n + DivisorSigma[0, n], {n, 1, m}]] (* Amiram Eldar, Nov 10 2021 *)

PARI

isok(n) = sum(k=1, n, k+numdiv(k) != n) == n; \\ Michel Marcus, Dec 08 2014