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A073348
Least k such that sigma(k)/k >= sigma(n)/n.
1
1, 2, 2, 4, 2, 6, 2, 6, 2, 6, 2, 12, 2, 4, 4, 6, 2, 12, 2, 12, 4, 4, 2, 24, 2, 4, 2, 6, 2, 24, 2, 6, 2, 4, 2, 36, 2, 4, 2, 12, 2, 12, 2, 6, 4, 4, 2, 48, 2, 6, 2, 6, 2, 12, 2, 12, 2, 4, 2, 60, 2, 4, 4, 6, 2, 12, 2, 6, 2, 12, 2, 60, 2, 4, 4, 6, 2, 12, 2, 12, 2, 4, 2, 60, 2, 4, 2, 12, 2, 60, 2, 6, 2, 4
OFFSET
1,2
LINKS
FORMULA
It seems that Sum_{k=1..n} a(k) is asymptotic to C*n*log(n)*log(log(n)) with C>1.
MATHEMATICA
a[n_] := Module[{k = 1, r = DivisorSigma[-1, n]}, While[DivisorSigma[-1, k] < r, k++]; k]; Array[a, 100] (* Amiram Eldar, May 05 2022 *)
PROG
(PARI) a(n)=if(n<0, 0, s=1; while(sigma(s)/s<sigma(n)/n, s++); s)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Aug 23 2002
STATUS
approved