A141218 Write the n-th nonprime (A018252(n)) as a product of primes; decrease one copy of the largest prime by 1 and increase one copy of the smallest prime by 1, multiply the resulting numbers.

1, 3, 6, 6, 8, 12, 12, 18, 16, 12, 18, 24, 24, 30, 24, 24, 36, 24, 36, 36, 24, 40, 48, 36, 36, 54, 48, 48, 54, 60, 48, 66, 48, 48, 60, 64, 72, 54, 60, 72, 72, 84, 72, 90, 72, 48, 72, 90, 96, 88, 90, 72, 108, 80, 108, 80, 108, 96, 72, 120, 108, 96, 126, 112, 120, 108, 96, 132, 120

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 07 2008

Keywords

• nonn
• look

Examples

			1st nonprime = 1 (has no prime factors); a(1) = empty product = 1.
2nd nonprime = 4 = (p(max)=2)*(p(min)=2); a(2) = (2-1)*(2+1) = 1*3 = 3.
3rd nonprime = 6 = (p(max)=3)*(p(min)=2); a(3) = (3-1)*(2+1) = 2*3 = 6.
4th nonprime = 8 = (p(max)=2)*(p=2)*(p(min)=2); a(4) = (2-1)*2*(2+1) = 1*2*3 = 6.
		

Links

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

Crossrefs

Cf. A018252, A141553, A141554.

Programs

Maple

f:= proc(m) local F,p1,p2;
  if isprime(m) then return NULL fi;
  F:= numtheory:-factorset(m);
  p1:= min(F); p2:= max(F);
  m*(p1+1)/p1*(p2-1)/p2;
end proc:
1, seq(f(i),i=2..200); # Robert Israel, Oct 08 2018

Mathematica

npr={};Do[If[!PrimeQ[i],AppendTo[npr,i]],{i,2,93}];f[k_]:=k*(FactorInteger[k][[1,1]]+1)/FactorInteger[k][[1,1]]*(FactorInteger[k][[-1,1]]-1)/FactorInteger[k][[-1,1]];Join[{1},f/@npr] (* James C. McMahon, Jul 18 2025 *)

Extensions

Three terms corrected by R. J. Mathar, Aug 18 2008

Entry revised by N. J. A. Sloane, Mar 07 2014

Examples revised by Jon E. Schoenfield, Mar 08 2014