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A328313 For all such terms k in A143293 (partial sums of primorials) for which A129251(k) = 0, the term A276085(k) is included here.

%I A328313 #15 Oct 12 2019 19:06:52
%S A328313 2,4,2312,3217644767340672907899084554132
%N A328313 For all such terms k in A143293 (partial sums of primorials) for which A129251(k) = 0, the term A276085(k) is included here.
%C A328313 Construction: apply A276085 to the terms in the intersection of A143293 and A048103.
%C A328313 The next terms are quite big and can be found in the b-file. Note the nonmonotonic order, a(8) < a(5), a(6) and a(7).
%C A328313 A276086(a(n)) is in A143293, A276086(A276086(a(n))) is one of the primorials, A002110, and A276086(A276086(A276086(a(n)))) is a prime.
%C A328313 A327969(a(n)) <= 5 for all n.
%H A328313 Antti Karttunen, <a href="/A328313/b328313.txt">Table of n, a(n) for n = 1..8</a>
%o A328313 (PARI)
%o A328313 A002110(n) = prod(i=1,n,prime(i));
%o A328313 A143293(n) = if(n==0, 1, my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); (s)); \\ From A143293.
%o A328313 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A328313 A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A328313 k=0; for(n=1,12,t = A143293(n); u = A276085(t); if(A276086(u) == t, k++; print1(u,", ")));
%Y A328313 Cf. A002110, A048103, A129251, A143293, A276085, A276086, A327969, A328243.
%K A328313 nonn
%O A328313 1,1
%A A328313 _Antti Karttunen_, Oct 12 2019