A067293 - OEIS

A067293

Numbers k such that prime(k+1)-(k+1)*tau(k+1) = prime(k)-k*tau(k) where tau(k) = A000005(k) is the number of divisors of k.

2, 14, 38, 85, 93, 122, 135, 213, 243, 301, 387, 394, 537, 603, 694, 766, 778, 903, 963, 1041, 1083, 1265, 1346, 1354, 1382, 1401, 1412, 1706, 1713, 1729, 1882, 1981, 2077, 2126, 2306, 2540, 2644, 2685, 2697, 2702, 2854, 2874, 2986, 3068, 3081, 3117, 3310

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

MATHEMATICA

f[n_] := f[n] = Prime[n] - n * DivisorSigma[0, n]; Select[Range[3500], f[#] == f[#+1] &] (* Amiram Eldar, Apr 08 2024 *)

PROG

(PARI) f(n) = prime(n) - n * numdiv(n);

is(n) = f(n) == f(n+1); \\ Amiram Eldar, Apr 08 2024

CROSSREFS

Cf. A000005, A067292, A067335, A067355, A067356.