cp's OEIS Frontend

A067532 Numbers k such that k + number of divisors of k is a prime.

%I A067532 #24 Jul 02 2025 16:02:01
%S A067532 1,3,4,5,11,15,17,27,29,33,39,41,55,57,59,64,69,71,85,93,100,101,105,
%T A067532 107,123,133,137,145,149,159,165,175,177,179,187,189,191,197,219,227,
%U A067532 231,235,237,239,245,247,253,255,259,265,267,269,273,275,281,285,303
%N A067532 Numbers k such that k + number of divisors of k is a prime.
%C A067532 Smaller of the twin primes (A001359) is a term.
%H A067532 Michael De Vlieger, <a href="/A067532/b067532.txt">Table of n, a(n) for n = 1..10000</a>
%e A067532 a(1) = 1 (1+d(1) = 1+1 = 2 = prime).
%e A067532 a(2) = 3 (3+d(3) = 3+2 = 5 = prime).
%p A067532 with(numtheory): for n from 3 to 500 do if isprime(n+tau(n)) then printf(`%d,`,n) fi:od: # _James Sellers_, Feb 18 2002
%t A067532 a067532[n_] := Select[Range[n], PrimeQ[# + DivisorSigma[0, #]] &]; a067532[303] (* _Michael De Vlieger_, Dec 22 2014 *)
%o A067532 (PARI) isok(k) = isprime(k + numdiv(k)); \\ _Amiram Eldar_, Jan 27 2025
%Y A067532 Cf. A000005, A001359, A067531.
%K A067532 easy,nonn
%O A067532 1,2
%A A067532 _Amarnath Murthy_, Feb 17 2002
%E A067532 More terms from _James Sellers_, Feb 18 2002
%E A067532 Sequence corrected by _Juri-Stepan Gerasimov_, Oct 18 2009
%E A067532 Offset corrected by _N. J. A. Sloane_, Oct 21 2009
%E A067532 Corrected by _Charles R Greathouse IV_, Mar 19 2010