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.

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, 21, 30, 28, 27, 26, 42, 25, 40, 54, 35, 38, 30, 45, 52, 36, 42, 31, 42, 33, 54, 64, 60, 39, 38, 50, 45, 60, 39, 70, 42, 78, 45, 56, 90, 43, 54, 76, 45, 62, 52, 63, 90

Offset

1,2

Links

Table of n, a(n) for n=1..67.

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+2)*(2-1) = 4*1 = 4.
3rd nonprime = 6 = (p(max)=3)*(p(min)=2); a(3) = (3+2)*(2-1) = 5*1 = 5.
4th nonprime = 8 = (p(max)=2)*(p=2)*(p(min)=2); a(4) = (2+2)*2*(2-1) = 4*2*1 = 8.

Maple

From R. J. Mathar, Mar 29 2010: (Start)
A006530 := proc(n) if n = 1 then 1; else max(op(numtheory[factorset](n))) ; end if; end proc:
A020639 := proc(n) if n = 1 then 1; else min(op(numtheory[factorset](n))) ; end if; end proc:
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:
A052369 := proc(n) A006530(A002808(n)) ; end proc: A056608 := proc(n) A020639(A002808(n)) ; end proc:
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:
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)

Crossrefs

Sequence in context: A268128 A064394 A346457 * A340762 A092022 A346302

Adjacent sequences: A141217 A141218 A141219 * A141221 A141222 A141223

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 07 2008

Extensions

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

Status

approved