A376409 a(n) = A048675(A376408(n)); Partial sums of A376408.

0, 1, 3, 9, 99, 353529, 274407373885532679, 2443417474326613595267894539584266773823049253134356679026035220285823429

Offset: 0

Author

Antti Karttunen, Nov 04 2024

Keywords

• nonn

Comments

a(8) has 407 digits, a(9) has 2804 digits.

By induction, it is easy to see that formula a(n) = A048675(A376408(n)) implies that from the second term onward, this sequence gives the partial sums of A376408, as A048675 is fully additive.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A019565, A048675, A376407, A376408.

Cf. also A376401 (an analogous sequence for A276075).

Programs

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A376408(n) = if(!n,1,my(x=A376408(n-1)); x*A019565(x));
A376409(n) = A048675(A376408(n));

Formula

a(0) = 0; and for n >= 1, a(n) = a(n-1) + A376408(n-1) = Sum_{i=0..n-1} A376408(i).