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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.
6
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
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
KEYWORD
nonn,look
AUTHOR
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