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

1,2

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.

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A336374 A346669 A187929 * A359080 A103796 A368100

Adjacent sequences: A272869 A272870 A272871 * A272873 A272874 A272875

Keyword

nonn

Author

Altug Alkan, May 11 2016

Status

approved