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A376416 a(n) = A276085(A006862(n)), where A276085 is the primorial base log-function, and A006862 is the Euclid numbers, one more than primorials.

%I A376416 #17 Nov 17 2024 13:06:59
%S A376416 1,2,30,6469693230,
%T A376416 7799922041683461553249199106329813876687996789903550945093032474868511536164700810
%N A376416 a(n) = A276085(A006862(n)), where A276085 is the primorial base log-function, and A006862 is the Euclid numbers, one more than primorials.
%C A376416 Numbers k such that when we apply primorial base exp function (A276086) twice to them, the results are squarefree even semiprimes, A100484 after its initial 4. See comments in A377871.
%C A376416 a(5)..a(8) have 976, 209, 111, 12051 decimal digits.
%C A376416 a(n) is a primorial for those n that are in A014545, that is, when A006862(n) is one of the primorial primes, A018239.
%H A376416 Antti Karttunen, <a href="/A376416/b376416.txt">Table of n, a(n) for n = 0..7</a>
%H A376416 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A376416 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A376416 a(n) = A276085(1+A002110(n)) = A276085(A276085(A100484(1+n))).
%F A376416 For n >= 1, A276087(a(n)) = A100484(1+n).
%o A376416 (PARI)
%o A376416 A276085(n) = { my(f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= prime(i); i++); s += f[k, 2]*pr); (s); };
%o A376416 A376416(n) = A276085(1+prod(i=1,n,prime(i)));
%Y A376416 Cf. A002110, A006862, A014545, A018239, A100484, A276085, A276086, A276087, A377871.
%K A376416 nonn
%O A376416 0,2
%A A376416 _Antti Karttunen_, Nov 17 2024