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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.

%I A347101 #11 Apr 05 2022 17:07:30
%S A347101 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 A347101 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 A347101 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 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.
%H A347101 Antti Karttunen, <a href="/A347101/b347101.txt">Table of n, a(n) for n = 1..65537</a>
%H A347101 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A347101 For all n >= 0, a(2^n) = 1.
%o A347101 (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 A347101 Cf. A000079 (positions of 1's), A001223, A347102, A347123.
%K A347101 nonn,mult
%O A347101 1,3
%A A347101 _Antti Karttunen_, Aug 19 2021