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Numbers k such that k + number of divisors of k is a prime.
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%I #23 Jan 27 2025 02:24:49

%S 1,3,4,5,11,15,17,27,29,33,39,41,55,57,59,64,69,71,85,93,100,101,105,

%T 107,123,133,137,145,149,159,165,175,177,179,187,189,191,197,219,227,

%U 231,235,237,239,245,247,253,255,259,265,267,269,273,275,281,285,303

%N Numbers k such that k + number of divisors of k is a prime.

%C Smaller of the twin primes (A001359) is a term.

%H Michael De Vlieger, <a href="/A067532/b067532.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1 (1+d(1) = 1+1 = 2 = prime).

%e a(2) = 3 (3+d(3) = 3+2 = 5 = prime).

%p with(numtheory): for n from 3 to 500 do if isprime(n+tau(n)) then printf(`%d,`,n) fi:od: # _James A. Sellers_, Feb 18 2002

%t a067532[n_] := Select[Range[n], PrimeQ[# + DivisorSigma[0, #]] &]; a067532[303] (* _Michael De Vlieger_, Dec 22 2014 *)

%o (PARI) isok(k) = isprime(k + numdiv(k)); \\ _Amiram Eldar_, Jan 27 2025

%Y Cf. A000005, A001359, A067531.

%K easy,nonn,changed

%O 1,2

%A _Amarnath Murthy_, Feb 17 2002

%E More terms from _James A. Sellers_, Feb 18 2002

%E Sequence corrected by _Juri-Stepan Gerasimov_, Oct 18 2009

%E Offset corrected by _N. J. A. Sloane_, Oct 21 2009

%E Corrected by _Charles R Greathouse IV_, Mar 19 2010