cp's OEIS Frontend

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.

%I A141218 #31 Jul 18 2025 14:45:47
%S A141218 1,3,6,6,8,12,12,18,16,12,18,24,24,30,24,24,36,24,36,36,24,40,48,36,
%T A141218 36,54,48,48,54,60,48,66,48,48,60,64,72,54,60,72,72,84,72,90,72,48,72,
%U A141218 90,96,88,90,72,108,80,108,80,108,96,72,120,108,96,126,112,120,108,96,132,120
%N 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.
%H A141218 Robert Israel, <a href="/A141218/b141218.txt">Table of n, a(n) for n = 1..10000</a>
%e A141218 1st nonprime = 1 (has no prime factors); a(1) = empty product = 1.
%e A141218 2nd nonprime = 4 = (p(max)=2)*(p(min)=2); a(2) = (2-1)*(2+1) = 1*3 = 3.
%e A141218 3rd nonprime = 6 = (p(max)=3)*(p(min)=2); a(3) = (3-1)*(2+1) = 2*3 = 6.
%e A141218 4th nonprime = 8 = (p(max)=2)*(p=2)*(p(min)=2); a(4) = (2-1)*2*(2+1) = 1*2*3 = 6.
%p A141218 f:= proc(m) local F,p1,p2;
%p A141218   if isprime(m) then return NULL fi;
%p A141218   F:= numtheory:-factorset(m);
%p A141218   p1:= min(F); p2:= max(F);
%p A141218   m*(p1+1)/p1*(p2-1)/p2;
%p A141218 end proc:
%p A141218 1, seq(f(i),i=2..200); # _Robert Israel_, Oct 08 2018
%t A141218 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 *)
%Y A141218 Cf. A018252, A141553, A141554.
%K A141218 nonn,look
%O A141218 1,2
%A A141218 _Juri-Stepan Gerasimov_, Aug 07 2008
%E A141218 Three terms corrected by _R. J. Mathar_, Aug 18 2008
%E A141218 Entry revised by _N. J. A. Sloane_, Mar 07 2014
%E A141218 Examples revised by _Jon E. Schoenfield_, Mar 08 2014