A376401 a(n) = A276075(A376400(n)); Partial sums of A376400.

0, 1, 3, 9, 39, 1089, 70814494839, 7568077812763134673885891483463343434987134201379042046671543939118568810481776089

Offset: 0

Author

Antti Karttunen, Nov 02 2024

Keywords

• nonn

Comments

a(8) has 2129 (decimal) digits.

From the second term onward also the partial sums of A376400.

By induction, it is easy to see that formula a(n) = A276075(A376400(n)) implies that from the second term onward, this sequence gives the partial sums of A376400, as A276075 is fully additive.

Links

• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A276075, A276076, A376400, A376403.

Cf. also A143293 (when prepended with 0, an analogous sequence for A276085).

Programs

PARI

A276075(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*(primepi(f[k, 1])!)); };
A276076(n) = { my(m=1, p=2, i=2); while(n, m *= (p^(n%i)); n = n\i; p = nextprime(1+p); i++); (m); };
A376400(n) = if(!n,1,my(x=A376400(n-1)); x*A276076(x));
A376401(n) = A276075(A376400(n));
\\ Or alternatively as:
A376401(n) = if(!n,0,A376401(n-1)+A376400(n-1));

Formula

a(0) = 0; and for n >= 1, a(n) = a(n-1) + A376400(n-1) = Sum_{i=0..n-1} A376400(i).