A272872 Numbers k such that k+1 is divisible by number of divisors of k.

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 27, 29, 31, 35, 37, 39, 41, 43, 47, 51, 53, 55, 59, 61, 67, 71, 73, 79, 83, 87, 89, 91, 95, 97, 101, 103, 107, 109, 111, 113, 115, 119, 123, 127, 131, 135, 137, 139, 143, 149, 151, 155, 157, 159, 163, 167

Offset: 1

Author

Altug Alkan, May 11 2016

Keywords

• nonn

Comments

Inspired by A272353.

All odd primes are obvious members.

Numbers k such that k == -1 (mod A000005(k)). Nonprime terms are listed in A354714. - Max Alekseyev, Jun 04 2022

63 is the least number that is not in this sequence but is a member of A187929.

Examples

			15 is a term because A000005(15) = 4 divides 15+1 = 16.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Claudia A. Spiro, How Often Does the Number of Divisors of an Integer Divide Its Successor?, J. London Math. Soc. (1985) s2-31 (1): 30-40.

Crossrefs

Cf. A000005, A187929, A272353, A033950, A354711, A354712, A354714, A354715, A354716.

Programs

Mathematica

Select[Range@167, Mod[#+1, DivisorSigma[0, #]] == 0 &] (* Giovanni Resta, May 21 2016 *)

PARI

lista(nn) = {for(n=1, nn, if((n+1) % numdiv(n) == 0, print1(n, ", ")));}