A272337 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.

3, 4, 52, 164, 275, 332, 388, 556, 668, 724, 892, 1004, 1172, 1228, 1396, 1676, 1732, 1844, 2012, 2348, 2404, 2572, 2908, 3076, 3188, 3244, 3356, 3412, 3524, 3748, 4084, 4196, 4252, 4364, 4868, 4924, 5036, 5204, 5596, 5708, 5932, 6044, 6212, 6268, 6436, 6548

Offset: 1

Author

Paolo P. Lava, Apr 26 2016

Keywords

• nonn
• easy

Examples

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

Crossrefs

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

Programs

Maple

with(numtheory): P:=proc(q) local n;
for n from 1 to q do if (n*(n+1)/2) mod sigma(n)=tau(n) then print(n); fi;
od; end: P(10^6);

Mathematica

Select[Range@ 6600, Function[n, Mod[Total@ First@ #, Total@ Last@ #] == Length@ Last@ # &@ {Complement[Range@ n, #], #} &@ Divisors@ n]] (* faster, or *)
Select[Range@ 6600, Mod[Total[Select[Range[# - 1], Function[m, ! Divisible[#, m]]]], DivisorSigma[1, #]] == DivisorSigma[0, #] &] (* Michael De Vlieger, Apr 27 2016 *)

PARI

isok(n) = n*(n+1)/2 % sigma(n) == numdiv(n); \\ Michel Marcus, Apr 29 2016

Formula

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