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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.
1
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
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
Intersection of A036434 and A045765.
Sequence in context: A363518 A038522 A267435 * A186293 A158865 A139570
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Sep 29 2021
STATUS
approved