cp's OEIS Frontend

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

%I A272872 #43 Jun 04 2022 09:45:07
%S A272872 1,3,5,7,11,13,15,17,19,23,27,29,31,35,37,39,41,43,47,51,53,55,59,61,
%T A272872 67,71,73,79,83,87,89,91,95,97,101,103,107,109,111,113,115,119,123,
%U A272872 127,131,135,137,139,143,149,151,155,157,159,163,167
%N A272872 Numbers k such that k+1 is divisible by number of divisors of k.
%C A272872 Inspired by A272353.
%C A272872 All odd primes are obvious members.
%C A272872 Numbers k such that k == -1 (mod A000005(k)). Nonprime terms are listed in A354714. - _Max Alekseyev_, Jun 04 2022
%C A272872 63 is the least number that is not in this sequence but is a member of A187929.
%H A272872 Amiram Eldar, <a href="/A272872/b272872.txt">Table of n, a(n) for n = 1..10000</a>
%H A272872 Claudia A. Spiro, <a href="https://doi.org/10.1112/jlms/s2-31.1.30">How Often Does the Number of Divisors of an Integer Divide Its Successor?</a>, J. London Math. Soc. (1985) s2-31 (1): 30-40.
%e A272872 15 is a term because A000005(15) = 4 divides 15+1 = 16.
%t A272872 Select[Range@167, Mod[#+1, DivisorSigma[0, #]] == 0 &] (* _Giovanni Resta_, May 21 2016 *)
%o A272872 (PARI) lista(nn) = {for(n=1, nn, if((n+1) % numdiv(n) == 0, print1(n, ", ")));}
%Y A272872 Cf. A000005, A187929, A272353, A033950, A354711, A354712, A354714, A354715, A354716.
%K A272872 nonn
%O A272872 1,2
%A A272872 _Altug Alkan_, May 11 2016