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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.
5
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
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
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Feb 24 2002
STATUS
approved