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

1,2

Comments

Invented by the HR concept formation program.

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

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A036431, A036438, A062249.

Sequence in context: A164910 A276583 A135736 * A298795 A140400 A190430

Adjacent sequences: A036431 A036432 A036433 * A036435 A036436 A036437

Keyword

nonn

Author

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

Status

approved