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

0, 1, 2, 3, 6, 9, 4, 5, 10, 15, 30, 45, 20, 25, 50, 75, 150, 225, 100, 125, 250, 375, 750, 1125, 500, 625, 1250, 1875, 3750, 5625, 6, 7, 14, 21, 42, 63, 28, 35, 70, 105, 210, 315, 140, 175, 350, 525, 1050, 1575, 700, 875, 1750, 2625, 5250, 7875, 3500, 4375, 8750, 13125, 26250, 39375, 42, 49, 98, 147

Offset: 0

Author

Antti Karttunen, Dec 02 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A002110, A053669, A060681, A276084, A276086, A324895.

Cf. also A353528, A353529.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A060681(n) = (n-A032742(n));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A358764(n) = A060681(A276086(n));

PARI

A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A358764(n) = if(!n, n, if(n%6, A276086(n-1), my(p=A053669(n)); ((p-1)/p)*A276086(n)));

Formula

a(n) = A060681(A276086(n)).

a(n) = A276086(n) - A324895(n).

For n >= 1, a(n) = A276086(n) - (A276086(n) / A053669(n)).

When n > 0 and A276084(n) is:

< 2 (i.e., when n is not a multiple of 6), then a(n) = A276086(n-1),

2 (n is multiple of 6, but not of 30), then a(n) = 2*A276086(n-5),

3 (multiple of 30, but not of 210), then a(n) = A276086(n-27),

4 (multiple of 210, but not of 2310), then a(n) = A276086(n-203),

5 (multiple of 2310, but not of 30030), then a(n) = 2*A276086(n-2307),

6 (multiple of 30030, but not of 510510), then a(n) = 8*A276086(n-30029),

7 (multiple of 510510, but not of 9699690), then a(n) = A276086(n-510505),

8 (multiple of 9699690, but not of A002110(9)), then a(n) = A276086(n-9699479).