A074753 - OEIS

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A074753

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

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)

	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 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`
	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: A320033 A064047 A111899 * A013928 A172104 A006161` `Adjacent sequences: A074750 A074751 A074752 * A074754 A074755 A074756`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre, Sep 28 2002`
	STATUS	`approved`

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Last modified November 16 08:56 EST 2018. Contains 317268 sequences. (Running on oeis4.)