A272337 - OEIS

%I #11 Apr 29 2016 17:32:37

%S 3,4,52,164,275,332,388,556,668,724,892,1004,1172,1228,1396,1676,1732,

%T 1844,2012,2348,2404,2572,2908,3076,3188,3244,3356,3412,3524,3748,

%U 4084,4196,4252,4364,4868,4924,5036,5204,5596,5708,5932,6044,6212,6268,6436,6548

%N Numbers such that antisigma(n) mod sigma(n) = d(n), where antisigma(n) is the sum of the numbers less than n that do not divide n, sigma(n) is the sum of the divisors of n and d(n) is the number of divisors of n.

%F Solutions of the equation  A024816(n) mod A000203(n) = A000005(n).

%e 52*53/2 mod sigma(52) = 1378 mod 98 = 6 = d(52).

%p with(numtheory): P:=proc(q) local n;

%p for n from 1 to q do if (n*(n+1)/2) mod sigma(n)=tau(n) then print(n); fi;

%p od; end: P(10^6);

%t Select[Range@ 6600, Function[n, Mod[Total@ First@ #, Total@ Last@ #] == Length@ Last@ # &@ {Complement[Range@ n, #], #} &@ Divisors@ n]] (* faster, or *)

%t Select[Range@ 6600, Mod[Total[Select[Range[# - 1], Function[m, ! Divisible[#, m]]]], DivisorSigma[1, #]] == DivisorSigma[0, #] &] (* _Michael De Vlieger_, Apr 27 2016 *)

%o (PARI) isok(n) = n*(n+1)/2 % sigma(n) == numdiv(n); \\ _Michel Marcus_, Apr 29 2016

%Y Cf. A000005, A000203, A024816, A232324, A272338.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Apr 26 2016