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

2, 4, 2312, 3217644767340672907899084554132

Offset: 1

Author

Antti Karttunen, Oct 12 2019

Keywords

• nonn

Comments

Construction: apply A276085 to the terms in the intersection of A143293 and A048103.

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).

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.

A327969(a(n)) <= 5 for all n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8

Crossrefs

Cf. A002110, A048103, A129251, A143293, A276085, A276086, A327969, A328243.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A143293(n) = if(n==0, 1, my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); (s)); \\ From A143293.
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
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; };
k=0; for(n=1,12,t = A143293(n); u = A276085(t); if(A276086(u) == t, k++; print1(u,", ")));