A353666 - OEIS

%I #11 May 07 2022 16:33:41

%S 1,1,1,1,1,2,1,1,1,2,1,4,1,2,3,1,1,1,1,2,1,2,1,4,1,2,1,28,1,2,1,1,3,2,

%T 1,1,1,2,1,10,1,2,1,4,3,2,1,4,1,1,3,2,1,2,1,8,1,2,1,4,1,2,1,1,1,2,1,2,

%U 3,2,1,1,1,2,1,4,1,2,1,2,1,2,1,28,1,2,3,4,1,2,7,4,1,2,5,4,1,1,3,1,1,2,1,2,3

%N a(n) = gcd(n, A351546(n)).

%H Antti Karttunen, <a href="/A353666/b353666.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/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = gcd(n, A351546(n)).

%F a(n) = n / A353667(n) = A351546(n) / A353668(n).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A351546(n) = { my(f=factor(sigma(n)), u=A003961(n)); prod(k=1, #f~, f[k, 1]^((0!=(u%f[k, 1]))*f[k, 2])); };

%o A353666(n) = gcd(n, A351546(n));

%Y Cf. A351546, A353667, A353668.

%Y Differs from A353688 for the first time at n = 28, 30, 40, 60, 66, 84, 90, 102, 120, ...

%K nonn

%O 1,6

%A _Antti Karttunen_, May 04 2022