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A272872
Numbers k such that k+1 is divisible by number of divisors of k.
7
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
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, ", "))); }
KEYWORD
nonn
AUTHOR
Altug Alkan, May 11 2016
STATUS
approved