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A074753
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Number of integers k such that sigma(k) < n.
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7
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0, 1, 1, 2, 3, 3, 4, 5, 6, 6, 6, 6, 8, 9, 10, 11, 11, 11, 13, 13, 14, 14, 14, 14, 17, 17, 17, 17, 18, 18, 19, 21, 23, 23, 23, 23, 24, 24, 25, 26, 27, 27, 30, 30, 31, 31, 31, 31, 34, 34, 34, 34, 34, 34, 36, 36, 38, 39, 39, 39, 42, 42, 43, 44, 44, 44, 44, 44, 45, 45, 45, 45, 50, 50
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = card( k : sigma(k) < n ); a(n) is asymptotic to c*n with c=0.67...
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MAPLE
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N:= 100: # to get a(1)..a(N)
V:= Vector(N):
for n from 1 to N-2 do
s:= numtheory:-sigma(n)+1;
if s <= N then V[s]:= V[s]+1 fi;
od:
ListTools:-PartialSums(V); # Robert Israel, Jan 08 2018
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MATHEMATICA
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Table[Length[Select[Range[n], DivisorSigma[1, #] < n&]], {n, 1, 100}] (* Vaclav Kotesovec, Feb 16 2019 *)
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PROG
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(PARI) a(n)=sum(i=1, n, if(1+sign(sigma(i)-n), 0, 1))
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CROSSREFS
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Partial sums of A054973.
Cf. A000203.
Sequence in context: A320033 A064047 A111899 * A013928 A172104 A006161
Adjacent sequences: A074750 A074751 A074752 * A074754 A074755 A074756
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Sep 28 2002
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STATUS
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approved
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