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

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.

Sequence in context: A254964 A108597 A062548 * A009368 A092344 A281711

Adjacent sequences: A067290 A067291 A067292 * A067294 A067295 A067296

Keyword

nonn,easy

Author

Benoit Cloitre, Feb 24 2002

Status

approved