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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Intersection of A036434 and A045765.

Sequence in context: A363518 A038522 A267435 * A186293 A158865 A139570

Adjacent sequences: A348090 A348091 A348092 * A348094 A348095 A348096

Keyword

nonn

Author

Ctibor O. Zizka, Sep 29 2021

Status

approved