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 A132995 a(n) = gcd(sum{k=1...n} p(k), product{j=1...n} p(j)), where p(k) is the k-th prime. 2
 2, 1, 10, 1, 14, 1, 2, 77, 10, 3, 10, 1, 238, 1, 82, 3, 110, 3, 2, 213, 2, 7, 874, 3, 530, 129, 158, 3, 370, 177, 430, 3, 994, 3, 2, 3, 646, 2747, 2914, 21, 3266, 3, 3638, 3, 2014, 3, 14, 4661, 1222, 5117, 1070, 69, 5830, 3, 2, 6601, 6870, 7141, 2, 1, 26, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From M. F. Hasler, Mar 10 2014: (Start) The terms a(n) must have the same parity as the sum of the first n primes, A007504(n), which is the opposite of the parity of the index n. Otherwise said, the sequence equals 0,1,0,1,0,1... (mod 2). The since the terms of this sequence are divisors of primorials A002110, they are squarefree numbers, A005117. Is it true, and if so, can it be proved that * all of the squarefree numbers do appear? * all of the squarefree numbers do appear infinitely often? At least it seems that this is the case for the terms 1, 2 and 3. (End) A239070(n) = position of first occurrence of n-th squarefree number in this sequence. - Reinhard Zumkeller, Mar 10 2014 LINKS M. F. Hasler and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 9592 terms from M. F. Hasler) FORMULA A132995(n) = gcd(A007504(n), A002110(n)). - M. F. Hasler, Mar 10 2014 EXAMPLE The first 7 primes are 2,3,5,7,11,13,17. 2+3+5+7+11+13+17 = 58 = 2*29. So a(7) = gcd(58, 2*3*5*7*11*13*17) = 2. MAPLE seq(gcd(add(ithprime(i), i=1..n), mul(ithprime(j), j=1..n)), n=1..50); # Emeric Deutsch, Nov 24 2007 # second Maple program: with(numtheory): s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+ithprime(n)) end: a:= n-> mul(`if`(i<=ithprime(n), i, 1), i=factorset(s(n))): seq(a(n), n=1..100);  # Alois P. Heinz, Mar 10 2014 MATHEMATICA nn=60; With[{prs=Prime[Range[nn]]}, Table[GCD[Total[Take[prs, n]], Times@@Take[ prs, n]], {n, nn}]] (* Harvey P. Dale, May 07 2011 *) PROG (PARI) c=s=0; forprime(p=2, 1e5, f=factor(s+=p, p); f[, 2]=apply(t->t<=p, f[, 1]); write("/tmp/b132995.txt", c++" "factorback(f))) \\ M. F. Hasler, Mar 09 2014 (Haskell) a132995 n = a132995_list !! (n-1) a132995_list = tail \$ f a000040_list 0 1 where    f (p:ps) u v = (gcd u v) : f ps (p + u) (p * v) -- Reinhard Zumkeller, Mar 09 2014 CROSSREFS Cf. A007504, A002110. Sequence in context: A074951 A055633 A105606 * A114692 A112691 A110169 Adjacent sequences:  A132992 A132993 A132994 * A132996 A132997 A132998 KEYWORD nonn,look AUTHOR Leroy Quet, Nov 22 2007 EXTENSIONS More terms from Emeric Deutsch, Nov 24 2007 STATUS approved

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Last modified May 28 12:02 EDT 2020. Contains 334681 sequences. (Running on oeis4.)