A348093 Numbers k >= 1 such that there is no pair (x,y) such that x - d(x) = k or y + d(y) = k, where d = A000005 = number of divisors.

8, 20, 36, 40, 67, 68, 79, 88, 100, 116, 117, 131, 132, 134, 140, 156, 164, 167, 180, 185, 196, 204, 228, 244, 252, 268, 276, 284, 300, 308, 312, 321, 324, 341, 348, 370, 372, 379, 388, 401, 405, 408, 420, 425, 436, 439, 453, 460, 476, 479

Offset: 1

Author

Ctibor O. Zizka, Sep 29 2021

Keywords

• nonn

Comments

Numbers k >= 1 such that A060990(k) + A036431(k) = 0.

Examples

			k = 8 is a term: there are no x,y such that x - d(x) = 8, y + d(y) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A036431, A049820, A060990, A062249.

Intersection of A036434 and A045765.

Programs

Mathematica

With[{max = 480}, Complement[Range[max], Select[Union[Flatten[Table[n + DivisorSigma[0, n]*{-1, 1}, {n, 1, max + 2 + 2*Ceiling[Sqrt[2*max+4]]}]]], # <= max &]]] (* Amiram Eldar, Mar 04 2023 *)

PARI

okp(k) = sum(i=1, k, i+numdiv(i) == k) == 0;
okm(k) = sum(i=1, 2*k+2, i-numdiv(i) == k) == 0;
isok(k) = okp(k) && okm(k); \\ Michel Marcus, Oct 01 2021