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 A070172 Smallest k such that sigma(k) >= n. 3
 1, 2, 2, 3, 4, 4, 4, 6, 6, 6, 6, 6, 8, 8, 8, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 36, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also smallest m to partition n into distinct divisors of m; highly abundant numbers are record values: a(i) < A002093(n) for 1<=i < A085443(n), A002093(n)=a(A085443(n)). - Reinhard Zumkeller, Jun 30 2003 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA It seems that lim n -> infinity a(n)/n*log(log(n))=C=0.6... MATHEMATICA nn=80; With[{s=Table[{n, DivisorSigma[1, n]}, {n, nn}]}, Transpose[ Flatten[ Table[ Select[s, #[[2]]>=i&, 1], {i, nn}], 1]][[1]]] (* Harvey P. Dale, Dec 28 2013 *) PROG (PARI) for(n=1, 150, s=1; while(sigma(s)

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Last modified May 16 11:33 EDT 2021. Contains 343942 sequences. (Running on oeis4.)