A079449 Primes p such that there is at least one integer x satisfying p = x*tau(x)+1 where tau(x) = A000005(x), the number of divisors of x.

2, 5, 7, 11, 13, 23, 41, 47, 59, 61, 73, 83, 89, 107, 109, 137, 157, 167, 179, 193, 227, 229, 233, 241, 263, 271, 277, 313, 337, 347, 349, 359, 373, 379, 383, 409, 433, 449, 457, 461, 467, 479, 503, 563, 569, 587, 709, 719, 733, 809, 821, 839, 853, 857, 863

Offset: 1

Author

Benoit Cloitre, Jan 13 2003

Keywords

• nonn

Examples

			12*tau(12) = 72 hence 73 is in the sequence.
		

Links

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

Crossrefs

Cf. A000005, A079448, A083271.

Programs

Mathematica

seq[lim_] := Union[Select[Table[k * DivisorSigma[0, k] + 1, {k, 1, Floor[lim/2]}], # <= lim && PrimeQ[#] &]]; seq[1000] (* Amiram Eldar, Apr 19 2025 *)

PARI

lista(nn) = {forprime(p=2, nn, for (n=1, p, if (n*numdiv(n)+1 == p, print1(p, ", "); break;);););} \\ Michel Marcus, Dec 01 2013