A347101 - OEIS

%I #11 Apr 05 2022 17:07:30

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A347101/b347101.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

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

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

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

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, Aug 19 2021