A070172 - OEIS

A070172

Smallest k such that sigma(k) >= n.

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

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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)<n, s++); print1(s, ", "))

CROSSREFS

Cf. A002093.

Sequence in context: A224709 A309965 A366385 * A273353 A367410 A259197

Adjacent sequences: A070169 A070170 A070171 * A070173 A070174 A070175

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 06 2002

STATUS

approved