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 A143201 Product of distances between prime factors in factorization of n. 16
 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 6, 3, 1, 1, 2, 1, 4, 5, 10, 1, 2, 1, 12, 1, 6, 1, 6, 1, 1, 9, 16, 3, 2, 1, 18, 11, 4, 1, 10, 1, 10, 3, 22, 1, 2, 1, 4, 15, 12, 1, 2, 7, 6, 17, 28, 1, 6, 1, 30, 5, 1, 9, 18, 1, 16, 21, 12, 1, 2, 1, 36, 3, 18, 5, 22, 1, 4, 1, 40, 1, 10, 13, 42, 27, 10, 1, 6, 7, 22 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(A007947(n)) = a(n); A006093 and A001747 give record values and where they occur: A006093(n)=a(A001747(n+1)) for n>1. a(n) = 1 iff n is a prime power: a(A000961(n))=1; a(n) = 2 iff n has exactly 2 and 3 as prime factors: a(A033845(n))=2; a(n) = 3 iff n is in A143202; a(n) = 4 iff n has exactly 2 and 5 as prime factors: a(A033846(n))=4; a(n) = 5 iff n is in A143203; a(n) = 6 iff n is in A143204; a(n) = 7 iff n is in A143205; a(n) <> A006512(k)+1 for k>1. a(A033849(n))=3; a(A033851(n))=3; a(A033850(n))=5; a(A033847(n))=6; a(A033848(n))=10. [Reinhard Zumkeller, Sep 19 2011] LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = f(n,1,1) where f(n,q,y) = if n=1 then y else if q=1 then f(n/p,p,1)) else f(n/p,p,y*(p-q+1)) with p = A020639(n) = smallest prime factor of n. EXAMPLE a(86) = a(43*2) = 43-2+1 = 42; a(138) = a(23*3*2) = (23-3+1)*(3-2+1) = 42; a(172) = a(43*2*2) = (43-2+1)*(2-2+1) = 42; a(182) = a(13*7*2) = (13-7+1)*(7-2+1) = 42; a(276) = a(23*3*2*2) = (23-3+1)*(3-2+1)*(2-2+1) = 42; a(330) = a(11*5*3*2) = (11-5+1)*(5-3+1)*(3-2+1) = 42. MATHEMATICA Table[Times@@(Differences[Flatten[Table[First[#], {Last[#]}]&/@ FactorInteger[ n]]]+1), {n, 100}] (* Harvey P. Dale, Dec 07 2011 *) PROG (Haskell) a143201 1 = 1 a143201 n = product \$ map (+ 1) \$ zipWith (-) (tail pfs) pfs    where pfs = a027748_row n -- Reinhard Zumkeller, Sep 13 2011 CROSSREFS Cf. A109313. Cf. A027748. Sequence in context: A174204 A118106 A324574 * A340082 A254048 A306671 Adjacent sequences:  A143198 A143199 A143200 * A143202 A143203 A143204 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 12 2008 STATUS approved

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Last modified April 10 23:13 EDT 2021. Contains 342877 sequences. (Running on oeis4.)