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

1,2

Links

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

Example

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.

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

Crossrefs

Cf. A018252, A141553, A141554.

Sequence in context: A178746 A229986 A025500 * A342425 A318845 A147866

Adjacent sequences: A141215 A141216 A141217 * A141219 A141220 A141221

Keyword

nonn,look

Author

Juri-Stepan Gerasimov, Aug 07 2008

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

Status

approved