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 A277368 Numbers such that the number of their divisors divide the sum of their aliquot parts. 1
 1, 4, 10, 16, 25, 26, 34, 56, 58, 60, 64, 74, 81, 82, 90, 96, 100, 106, 120, 121, 122, 132, 146, 178, 184, 194, 202, 204, 216, 218, 226, 234, 248, 274, 276, 289, 298, 306, 312, 314, 346, 348, 362, 364, 376, 386, 394, 408, 440, 458, 466, 480, 482, 492, 504, 514 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If p is a prime such that p == 2 (mod 3) then p^2 is a term. Bateman et al. (1981) proved that the asymptotic density of this sequence is 0. - Amiram Eldar, Jan 16 2020 REFERENCES Richard G. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, 2004, chapter 2, p. 76. LINKS Paolo P. Lava, Table of n, a(n) for n = 1..1000 Paul T. Bateman, Paul ErdÅ‘s, Carl Pomerance and E.G. Straus, The arithmetic mean of the divisors of an integer, in Marvin I. Knopp (ed.), Analytic Number Theory, Proceedings of a Conference Held at Temple University, Philadelphia, May 12-15, 1980, Lecture Notes in Mathematics, Vol. 899, Springer, Berlin - New York, 1981, pp. 197-220, alternative link. FORMULA Solutions k to A000005(k) | A001065(k). EXAMPLE sigma(26) - 26 = 42 - 26 = 16, d(26) = 4 and 16 / 4 = 4. MAPLE with(numtheory): P:= proc(q) local n; for n from 1 to q do if type((sigma(n)-n)/tau(n), integer) then print(n); fi; od; end: P(10^3); MATHEMATICA Select[Range@ 520, Mod[DivisorSigma[1, #] - #, DivisorSigma[0, #]] == 0 &] (* Michael De Vlieger, Oct 14 2016 *) PROG (PARI) isok(n) = ((sigma(n) - n) % numdiv(n)) == 0; \\ Michel Marcus, Oct 11 2016 (MAGMA) [k:k in [1..550]| (DivisorSigma(1, k)-k) mod DivisorSigma(0, k) eq 0]; // Marius A. Burtea, Jan 16 2020 CROSSREFS Cf. A000005, A001065, A003601, A047727. Sequence in context: A049881 A271911 A322948 * A067274 A331081 A054901 Adjacent sequences:  A277365 A277366 A277367 * A277369 A277370 A277371 KEYWORD nonn,easy AUTHOR Paolo P. Lava, Oct 11 2016 STATUS approved

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Last modified May 31 01:29 EDT 2020. Contains 334747 sequences. (Running on oeis4.)