A353667 - OEIS

%I #12 May 07 2022 16:33:44

%S 1,2,3,4,5,3,7,8,9,5,11,3,13,7,5,16,17,18,19,10,21,11,23,6,25,13,27,1,

%T 29,15,31,32,11,17,35,36,37,19,39,4,41,21,43,11,15,23,47,12,49,50,17,

%U 26,53,27,55,7,57,29,59,15,61,31,63,64,65,33,67,34,23,35,71,72,73,37,75,19,77,39,79,40,81,41,83,3

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

%H Antti Karttunen, <a href="/A353667/b353667.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A353667/a353667.txt">Data supplement: n, a(n) computed 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) = n / A353666(n) = n / gcd(n, A351546(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 A353667(n) = (n / gcd(n, A351546(n)));

%Y Cf. A000203, A003961, A351546, A353666, A353668.

%Y Differs from A098988 for the first time at n = 28, 30, 40, 60, 66, 84, 90, 102, 120, ...

%K nonn

%O 1,2

%A _Antti Karttunen_, May 04 2022