A331290 - OEIS

%I #10 Jan 15 2020 18:40:19

%S 1,1,1,2,1,2,1,1,1,2,1,1,1,2,2,2,1,1,1,1,2,2,1,1,2,2,1,1,1,1,1,1,2,2,

%T 2,4,1,2,2,1,1,1,1,1,1,2,1,1,1,1,2,1,1,2,2,4,2,2,1,1,1,2,3,2,1,3,1,1,

%U 2,1,1,1,1,2,1,1,2,3,1,1,1,2,1,2,1,2,2,4,1,2,2,1,2,2,1,2,1,1,1,1,1,3,1,4,1

%N a(n) = gcd(A001222(n), A329348(n)).

%C Records occur at n = 1, 4, 36, 112, 352, 1088, 2016, 2688, 8064, 63360, ...

%H Antti Karttunen, <a href="/A331290/b331290.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</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) = gcd(A001222(n), A329348(n)) = gcd(A001222(n), A331188(n) mod A117366(n)).

%F a(n) = gcd(A001222(n), A331289(n)).

%o (PARI)

%o A002110(n) = prod(i=1, n, prime(i));

%o A331290(n) = if(1==n, 1, my(f=factor(n), p=nextprime(1+vecmax(f[, 1]))); gcd((prod(i=1, #f~, A002110(primepi(f[i, 1]))^(f[i, 2]-(#f~==i)))%p),bigomega(n)));

%Y Cf. A001222, A002110, A117366, A329348, A331188, A331289, A331291.

%Y Cf. also A329618, A329621.

%K nonn,less

%O 1,4

%A _Antti Karttunen_, Jan 15 2020