A254572 Least multiple of n that is abundant or perfect (A023196).

6, 6, 6, 12, 20, 6, 28, 24, 18, 20, 66, 12, 78, 28, 30, 48, 102, 18, 114, 20, 42, 66, 138, 24, 100, 78, 54, 28, 174, 30, 186, 96, 66, 102, 70, 36, 222, 114, 78, 40, 246, 42, 258, 88, 90, 138, 282, 48, 196, 100, 102, 104, 318, 54, 220, 56, 114, 174, 354, 60

Offset: 1

Author

Jeppe Stig Nielsen, Feb 01 2015

Keywords

• nonn

Comments

See A254571(n) = a(n)/n for the multipliers.

Very often a(n) = A064162(n), but the definition of the latter requires strict abundance.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023196, A064162, A254571.

Programs

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*n fi od:
      6*n
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*n]], {k, {1, 2, 3, 4, 6}}];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 09 2023 *)

PARI

a(n) = forstep(m=n,6*n,n,if(sigma(m)>=2*m,return(m)))