A347101 Fully multiplicative with a(prime(k)) = A001223(k), where A001223 gives the distance from the k-th prime to the (k+1)-th prime.

1, 1, 2, 1, 2, 2, 4, 1, 4, 2, 2, 2, 4, 4, 4, 1, 2, 4, 4, 2, 8, 2, 6, 2, 4, 4, 8, 4, 2, 4, 6, 1, 4, 2, 8, 4, 4, 4, 8, 2, 2, 8, 4, 2, 8, 6, 6, 2, 16, 4, 4, 4, 6, 8, 4, 4, 8, 2, 2, 4, 6, 6, 16, 1, 8, 4, 4, 2, 12, 8, 2, 4, 6, 4, 8, 4, 8, 8, 4, 2, 16, 2, 6, 8, 4, 4, 4, 2, 8, 8, 16, 6, 12, 6, 8, 2, 4, 16, 8, 4, 2, 4, 4, 4, 16

Offset: 1

Author

Antti Karttunen, Aug 19 2021

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for primes, gaps between

Crossrefs

Cf. A000079 (positions of 1's), A001223, A347102, A347123.

Programs

PARI

A347101(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 1] = (nextprime(f[i, 1]+1)-f[i,1])); factorback(f); };

Formula

For all n >= 0, a(2^n) = 1.