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A002191
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Possible values for sum of divisors of n.
(Formerly M2318 N0916)
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48
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1, 3, 4, 6, 7, 8, 12, 13, 14, 15, 18, 20, 24, 28, 30, 31, 32, 36, 38, 39, 40, 42, 44, 48, 54, 56, 57, 60, 62, 63, 68, 72, 74, 78, 80, 84, 90, 91, 93, 96, 98, 102, 104, 108, 110, 112, 114, 120, 121, 124, 126, 127, 128, 132, 133, 138, 140, 144, 150, 152, 156
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OFFSET
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1,2
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COMMENTS
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Distinct values attained by the sigma(n) function, in ascending order.
The asymptotic density of this sequence is 0 (Niven, 1951, Rao and Murty, 1979). - Amiram Eldar, Jul 23 2020
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REFERENCES
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J. W. L. Glaisher, Number-Divisor Tables. British Assoc. Math. Tables, Vol. 8, Camb. Univ. Press, 1940, p. 85.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. Sita Rama Chandra Rao and G. Sri Rama Chandra Murty, On a theorem of Niven, Canadian Mathematical Bulletin, Vol 22, No. 1 (1979), pp. 113-115.
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FORMULA
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a(n)/n < log_10(n) + O(1) with O(1) <= 1 for all n. - M. F. Hasler, Nov 22 2019
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EXAMPLE
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a(100) = 272, a(10^3) = 3696, a(10^4) = 44496, a(10^5) = 510356, a(10^6) = 5691216. - M. F. Hasler, Nov 22 2019
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MAPLE
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N:= 1000: # to get all entries <= N
select(`<=`, {seq(numtheory[sigma](i), i=1..N)}, N); # Robert Israel, Jun 16 2014
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MATHEMATICA
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lim=1000; Select[Union[DivisorSigma[1, Range[lim]]], #<=lim &] (* T. D. Noe, May 06 2010 *)
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PROG
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(PARI) A002191_upto(N, M=N\1+1)=Set(apply(t->min(sigma(t), M), [1..N\1-1]))[^-1] \\ Needs big stack for N >= 10^6; slower alternative: {A002191_upto(N)= my(L=List(1), s); for(n=2, N\=1, N<(s=sigma(n))||listput(L, s)); Set(L)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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