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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 24 11:15 EST 2024. Contains 370303 sequences. (Running on oeis4.)