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A093818 a(n) = gcd(A001008(n), n!).

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%I A093818 #12 Aug 28 2017 20:18:36
%S A093818 1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,5,1,3,1,5,1,1,1,1,1,1,1,1,1,1,
%T A093818 1,1,1,1,1,1,1,7,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A093818 1,1,1,1,1,1,1,1,11,1,1,11,1,1,1,11,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A093818 a(n) = gcd(A001008(n), n!).
%C A093818 Conjecture: every odd prime occurs as a term in the sequence.
%C A093818 Observation: Terms other than 1 are rare. Of the terms a(1) .. a(29524), only 187 are larger than one. Among these 187 terms, the following 50 distinct values occur: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 227, 257, 269, 509, 863, 919, 1049, 1331, 9409, 11881. Of these, all other are primes except 121 = 11*11, 1331 = 11*11*11, 9409 = 97*97 and 11881 = 109*109. - _Antti Karttunen_, Aug 28 2017
%H A093818 Antti Karttunen, <a href="/A093818/b093818.txt">Table of n, a(n) for n = 1..29524</a>
%o A093818 (PARI)
%o A093818 A001008(n) = numerator(sum(i=1, n, 1/i)); \\ This function from _Michael B. Porter_, Dec 08 2009
%o A093818 A093818(n) = gcd(A001008(n),n!); \\ _Antti Karttunen_, Aug 28 2017
%Y A093818 Cf. A001008, A060746.
%K A093818 easy,nonn
%O A093818 1,7
%A A093818 _Vladeta Jovovic_, May 20 2004
%E A093818 More terms from _David Wasserman_, Apr 20 2007
%E A093818 Name edited (A001008 substituted for "Wolstenholme") by _Antti Karttunen_, Aug 28 2017