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

1,1

Links

Table of n, a(n) for n=1..46.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A080073 A032840 A114694 * A132678 A166850 A317856

Adjacent sequences: A272334 A272335 A272336 * A272338 A272339 A272340

Keyword

nonn,easy

Author

Paolo P. Lava, Apr 26 2016

Status

approved