A141219 Write the n-th nonprime (A018252(n)) as a product of primes; increase one copy of the largest prime by 1 and decrease one copy of the smallest prime by 1, multiply the resulting numbers.

1, 3, 4, 6, 8, 6, 8, 8, 12, 12, 12, 12, 16, 12, 16, 24, 14, 24, 16, 18, 24, 24, 18, 32, 24, 20, 28, 24, 24, 24, 36, 24, 32, 48, 30, 36, 28, 36, 48, 32, 40, 30, 36, 32, 48, 48, 56, 36, 36, 48, 40, 48, 38, 60, 40, 72, 42, 48, 72, 42, 48, 72, 44, 60, 48, 54, 84

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 07 2008

Keywords

• nonn

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) = 3*1 = 3.
3rd nonprime = 6 = (p(max)=3)*(p(min)=2); a(3) = (3+1)*(2-1) = 4*1 = 4.
4th nonprime = 8 = (p(max)=2)*(p=2)*(p(min)=2); a(4) = (2+1)*2*(2-1) = 3*2*1 = 6.
		

Programs

Mathematica

lim=66;i=n=1; Until[i==lim,If[n-PrimePi[n]>i, nonp[i+1]=n; i++;n++,n++]]; f[k_]:=k*(FactorInteger[k][[1, 1]]-1)/FactorInteger[k][[1, 1]]*(FactorInteger[k][[-1, 1]]+1)/FactorInteger[k][[-1, 1]]; Join[{1}, f/@Array[nonp, lim-1, 2]] (* James C. McMahon, Jul 18 2025 *)

Extensions

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

Entry revised by Jon E. Schoenfield, Mar 09 2014, following revision of A141218 by N. J. A. Sloane