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A373989 a(n) = A276150(gcd(A108951(n), A373158(n))), where A276150 is the digit sum in primorial base, A108951 is fully multiplicative and A373158 is fully additive with a(p) = p# for prime p, where x# is the primorial A034386(x).

%I A373989 #7 Jun 26 2024 09:32:30
%S A373989 1,1,1,2,1,2,1,1,2,2,1,1,1,2,2,2,1,1,1,1,2,2,1,2,2,2,3,1,1,1,1,1,2,2,
%T A373989 2,4,1,2,2,2,1,1,1,1,1,2,1,1,2,1,2,1,1,2,6,4,2,2,1,4,1,2,1,2,6,1,1,1,
%U A373989 2,1,1,3,1,2,1,1,6,1,1,1,4,2,1,4,2,2,2,2,1,2,6,1,2,2,2,4,1,1,5,4,1,1,1,2,1
%N A373989 a(n) = A276150(gcd(A108951(n), A373158(n))), where A276150 is the digit sum in primorial base, A108951 is fully multiplicative and A373158 is fully additive with a(p) = p# for prime p, where x# is the primorial A034386(x).
%H A373989 Antti Karttunen, <a href="/A373989/b373989.txt">Table of n, a(n) for n = 1..100000</a>
%H A373989 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A373989 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A373989 a(n) = A276150(A373985(n)).
%o A373989 (PARI)
%o A373989 A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
%o A373989 A373985(n) = { my(f=factor(n),m=1,s=0); for(i=1, #f~, my(x=prod(i=1,primepi(f[i, 1]),prime(i))); s += f[i, 2]*x; m *= x^f[i, 2]); gcd(m,s); };
%o A373989 A373989(n) = A276150(A373985(n));
%Y A373989 Cf. A034386, A108951, A276150, A373158, A373985.
%Y A373989 Cf. also A324888.
%K A373989 nonn
%O A373989 1,4
%A A373989 _Antti Karttunen_, Jun 26 2024