A347123 Fully multiplicative with a(prime(k)) = prime(1+floor(A001223(k)/2)).

1, 2, 3, 4, 3, 6, 5, 8, 9, 6, 3, 12, 5, 10, 9, 16, 3, 18, 5, 12, 15, 6, 7, 24, 9, 10, 27, 20, 3, 18, 7, 32, 9, 6, 15, 36, 5, 10, 15, 24, 3, 30, 5, 12, 27, 14, 7, 48, 25, 18, 9, 20, 7, 54, 9, 40, 15, 6, 3, 36, 7, 14, 45, 64, 15, 18, 5, 12, 21, 30, 3, 72, 7, 10, 27, 20, 15, 30, 5, 48, 81, 6, 7, 60, 9, 10, 9, 24, 11, 54

Offset: 1

Author

Antti Karttunen, Aug 19 2021

Keywords

• nonn
• mult
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for primes, gaps between

Crossrefs

Cf. A001222, A001223, A003586, A007814, A347101, A347102.

Cf. also A336855.

Programs

PARI

A347123(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 1] = prime(1+((nextprime(f[i, 1]+1)-f[i,1])\2))); factorback(f); };

Formula

For all n >= 1, A001222(a(n)) = A001222(n), A007814(a(n)) = A007814(n).

For all n >= 1, a(A003586(n)) = A003586(n).