A376398 - OEIS

%I #8 Oct 28 2024 16:23:43

%S 0,1,3,5,11,14,44,47,51,58,268,272,2582,2613,2621,2625,32655,32660,

%T 543170,543178,543210,543421,10243111,10243116,10243128,10245439,

%U 10245445,10245477,233338347,233338356,6703031586,6703031591,6703031803,6703061834,6703061870,6703061876,207263552006,207264062517,207264064829,207264064838

%N a(n) = A276085(n!), where A276085 is the primorial base log-function.

%H Antti Karttunen, <a href="/A376398/b376398.txt">Table of n, a(n) for n = 1..2310</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A276085(A000142(n)).

%F a(n) = Sum_{i=1..n} A276085(i).

%o (PARI)

%o A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };

%o A376398(n) = A276085(n!);

%Y Partial sums of A276085.

%Y Cf. A000142, A002110.

%Y Cf. also A143293, A336415, A376397.

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 28 2024