The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A254571 Least multiplier k such that k*n is abundant or perfect (A023196). 2
 6, 3, 2, 3, 4, 1, 4, 3, 2, 2, 6, 1, 6, 2, 2, 3, 6, 1, 6, 1, 2, 3, 6, 1, 4, 3, 2, 1, 6, 1, 6, 3, 2, 3, 2, 1, 6, 3, 2, 1, 6, 1, 6, 2, 2, 3, 6, 1, 4, 2, 2, 2, 6, 1, 4, 1, 2, 3, 6, 1, 6, 3, 2, 3, 4, 1, 6, 3, 2, 1, 6, 1, 6, 3, 2, 3, 4, 1, 6, 1, 2, 3, 6, 1, 4, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A254572(n)=a(n)*n for the actual non-deficient numbers. The range is {1,2,3,4,6}. Clearly a(n) <= 6 because 6*n is abundant for any n. No n can have a(n)=5. Suppose otherwise. There exists a prime p smaller than 5 which does not divide n (if not, 6|n and a(n)=1). That prime p (either 2 or 3) will boost the abundancy more than does 5. In particular (sigma(p*n))/(p*n) > (sigma(5*n))/(5*n) >= 2, but then a(n) should be p, a contradiction. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(A023196(n)) = 1. - Michel Marcus, Feb 02 2015 MAPLE f:= proc(n) local k; uses numtheory; for k from 1 to 4 do if sigma(k*n)>=2*k*n then return k fi od: 6 end proc: map(f, [\$1..100]); # Robert Israel, Feb 10 2019 MATHEMATICA a[n_] := Do[If[DivisorSigma[1, k*n] >= 2*k*n, Return[k]], {k, {1, 2, 3, 4, 6}}]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 09 2023 *) PROG (PARI) a(n) = for(k=1, 6, if(sigma(k*n)>=2*k*n, return(k))) CROSSREFS Cf. A023196, A254572. Sequence in context: A068996 A068924 A106224 * A360562 A244815 A226579 Adjacent sequences: A254568 A254569 A254570 * A254572 A254573 A254574 KEYWORD nonn,easy AUTHOR Jeppe Stig Nielsen, Feb 01 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 27 02:29 EDT 2023. Contains 361553 sequences. (Running on oeis4.)