A373989 - OEIS

%I #7 Jun 26 2024 09:32:30

%S 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 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 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 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 Antti Karttunen, <a href="/A373989/b373989.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A276150(A373985(n)).

%o (PARI)

%o 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 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(n) = A276150(A373985(n));

%Y Cf. A034386, A108951, A276150, A373158, A373985.

%Y Cf. also A324888.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 26 2024