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

1,1

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.

Note that terms a(1) and a(8) are themselves in A048103, while a(2)..a(7) are not. - Antti Karttunen, Apr 06 2026

Links

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

Formula

a(n) = A276085(A143293(A394891(n))). - Antti Karttunen, Apr 06 2026

Prog

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

Crossrefs

Cf. A002110, A048103, A129251, A143293, A276085, A276086, A327969, A328243, A394891.

Sequence in context: A102064 A085638 A134718 * A048829 A070655 A006263

Adjacent sequences: A328310 A328311 A328312 * A328314 A328315 A328316

Keyword

nonn

Author

Antti Karttunen, Oct 12 2019

Status

approved