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A358764 Largest difference between consecutive divisors of A276086(n), where A276086 is the primorial base exp-function.

%I A358764 #18 Dec 03 2022 20:26:34
%S A358764 0,1,2,3,6,9,4,5,10,15,30,45,20,25,50,75,150,225,100,125,250,375,750,
%T A358764 1125,500,625,1250,1875,3750,5625,6,7,14,21,42,63,28,35,70,105,210,
%U A358764 315,140,175,350,525,1050,1575,700,875,1750,2625,5250,7875,3500,4375,8750,13125,26250,39375,42,49,98,147
%N A358764 Largest difference between consecutive divisors of A276086(n), where A276086 is the primorial base exp-function.
%H A358764 Antti Karttunen, <a href="/A358764/b358764.txt">Table of n, a(n) for n = 0..11550</a>
%H A358764 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A358764 a(n) = A060681(A276086(n)).
%F A358764 a(n) = A276086(n) - A324895(n).
%F A358764 For n >= 1, a(n) = A276086(n) - (A276086(n) / A053669(n)).
%F A358764 When n > 0 and A276084(n) is:
%F A358764   < 2 (i.e., when n is not a multiple of 6),      then a(n) = A276086(n-1),
%F A358764   2 (n is multiple of  6, but not of      30),    then a(n) = 2*A276086(n-5),
%F A358764   3 (multiple of      30, but not of     210),    then a(n) = A276086(n-27),
%F A358764   4 (multiple of     210, but not of    2310),    then a(n) = A276086(n-203),
%F A358764   5 (multiple of    2310, but not of   30030),    then a(n) = 2*A276086(n-2307),
%F A358764   6 (multiple of   30030, but not of  510510),    then a(n) = 8*A276086(n-30029),
%F A358764   7 (multiple of  510510, but not of 9699690),    then a(n) = A276086(n-510505),
%F A358764   8 (multiple of 9699690, but not of A002110(9)), then a(n) = A276086(n-9699479).
%o A358764 (PARI)
%o A358764 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A358764 A060681(n) = (n-A032742(n));
%o A358764 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A358764 A358764(n) = A060681(A276086(n));
%o A358764 (PARI)
%o A358764 A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
%o A358764 A358764(n) = if(!n, n, if(n%6, A276086(n-1), my(p=A053669(n)); ((p-1)/p)*A276086(n)));
%Y A358764 Cf. A002110, A053669, A060681, A276084, A276086, A324895.
%Y A358764 Cf. also A353528, A353529.
%K A358764 nonn
%O A358764 0,3
%A A358764 _Antti Karttunen_, Dec 02 2022