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

%I A376401 #14 Nov 04 2024 12:33:14
%S A376401 0,1,3,9,39,1089,70814494839,
%T A376401 7568077812763134673885891483463343434987134201379042046671543939118568810481776089
%N A376401 a(n) = A276075(A376400(n)); Partial sums of A376400.
%C A376401 a(8) has 2129 (decimal) digits.
%C A376401 From the second term onward also the partial sums of A376400.
%C A376401 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.
%H A376401 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A376401 a(0) = 0; and for n >= 1, a(n) = a(n-1) + A376400(n-1) = Sum_{i=0..n-1} A376400(i).
%o A376401 (PARI)
%o A376401 A276075(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*(primepi(f[k, 1])!)); };
%o A376401 A276076(n) = { my(m=1, p=2, i=2); while(n, m *= (p^(n%i)); n = n\i; p = nextprime(1+p); i++); (m); };
%o A376401 A376400(n) = if(!n,1,my(x=A376400(n-1)); x*A276076(x));
%o A376401 A376401(n) = A276075(A376400(n));
%o A376401 \\ Or alternatively as:
%o A376401 A376401(n) = if(!n,0,A376401(n-1)+A376400(n-1));
%Y A376401 Cf. A276075, A276076, A376400, A376403.
%Y A376401 Cf. also A143293 (when prepended with 0, an analogous sequence for A276085).
%K A376401 nonn
%O A376401 0,3
%A A376401 _Antti Karttunen_, Nov 02 2024