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a(n) = gcd(A108951(n), A373158(n)), where A108951 is fully multiplicative and A373158 is fully additive with a(p) = p# for prime p, where x# is the primorial A034386(x).
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%I #9 Jun 25 2024 20:19:12

%S 1,2,6,4,30,4,210,2,12,4,2310,2,30030,4,36,8,510510,2,9699690,2,36,4,

%T 223092870,12,60,4,18,2,6469693230,2,200560490130,2,12,4,60,16,

%U 7420738134810,4,12,12,304250263527210,2,13082761331670030,2,6,4,614889782588491410,2,420,2,36,2,32589158477190044730,4,180,24,36,4

%N a(n) = gcd(A108951(n), A373158(n)), where 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="/A373985/b373985.txt">Table of n, a(n) for n = 1..2048</a>

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

%F a(n) = gcd(A373158(n), A373984(n)).

%F a(n) = A108951(n) / A373987(n).

%F For n >= 2, a(n) = A373158(n) / A373986(n).

%F For n >= 1, a(A000040(n)) = A002110(n).

%o (PARI) 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); };

%Y Cf. A000040, A002110, A034386, A108951, A373158, A373984, A373986, A373987.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 25 2024