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A141220 Write the n-th nonprime (A018252(n)) as a product of primes; increase one copy of the largest prime by 2 and decrease one copy of the smallest prime by 1, multiply the resulting numbers. 4

%I

%S 1,4,5,8,10,7,10,9,14,16,15,14,18,13,20,28,15,30,18,21,32,26,19,36,30,

%T 21,30,28,27,26,42,25,40,54,35,38,30,45,52,36,42,31,42,33,54,64,60,39,

%U 38,50,45,60,39,70,42,78,45,56,90,43,54,76,45,62,52,63,90

%N Write the n-th nonprime (A018252(n)) as a product of primes; increase one copy of the largest prime by 2 and decrease one copy of the smallest prime by 1, multiply the resulting numbers.

%e 1st nonprime = 1 (has no prime factors); a(1) = empty product = 1.

%e 2nd nonprime = 4 = (p(max)=2)*(p(min)=2); a(2) = (2+2)*(2-1) = 4*1 = 4.

%e 3rd nonprime = 6 = (p(max)=3)*(p(min)=2); a(3) = (3+2)*(2-1) = 5*1 = 5.

%e 4th nonprime = 8 = (p(max)=2)*(p=2)*(p(min)=2); a(4) = (2+2)*2*(2-1) = 4*2*1 = 8.

%p From _R. J. Mathar_, Mar 29 2010: (Start)

%p A006530 := proc(n) if n = 1 then 1; else max(op(numtheory[factorset](n))) ; end if; end proc:

%p A020639 := proc(n) if n = 1 then 1; else min(op(numtheory[factorset](n))) ; end if; end proc:

%p A002808 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do; end if; end proc:

%p A052369 := proc(n) A006530(A002808(n)) ; end proc: A056608 := proc(n) A020639(A002808(n)) ; end proc:

%p A141220 := proc(n) if n = 0 then 1; else c := A002808(n) ; hi := A052369(n) ; lo := A056608(n) ; c*(hi+2)*(lo-1)/lo/hi ; end if; end proc:

%p printf("1,") ; for n from 1 to 400 do a := A141220(n) ; if not isprime(a) then printf("%d,",a) ; end if; end do: (End)

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Aug 07 2008

%E Entry revised by _Jon E. Schoenfield_, Mar 09 2014, following revision of A141218 by _N. J. A. Sloane_

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Last modified July 23 21:46 EDT 2021. Contains 346265 sequences. (Running on oeis4.)