

A074753


Number of integers k such that sigma(k) < n.


8



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
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OFFSET

1,4


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = card( k : sigma(k) < n ); a(n) is asymptotic to c*n with c=0.67...


MAPLE

N:= 100: # to get a(1)..a(N)
V:= Vector(N):
for n from 1 to N2 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


MATHEMATICA

Table[Length[Select[Range[n], DivisorSigma[1, #] < n&]], {n, 1, 100}] (* Vaclav Kotesovec, Feb 16 2019 *)


PROG

(PARI) a(n)=sum(i=1, n, if(1+sign(sigma(i)n), 0, 1))


CROSSREFS

Partial sums of A054973.
Cf. A000203.
Sequence in context: A064047 A335152 A111899 * A013928 A172104 A006161
Adjacent sequences: A074750 A074751 A074752 * A074754 A074755 A074756


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Sep 28 2002


STATUS

approved



