A365457 - OEIS

%I #12 Sep 11 2023 15:52:48

%S 1,1,5,1,3,11,1,1,17,19,7,23,25,9,29,1,11,35,37,13,41,43,15,47,49,17,

%T 53,55,19,59,61,1,65,67,23,71,73,25,77,79,27,83,85,29,89,7,31,95,97,

%U 11,101,103,35,107,109,37,113,115,3,17,11,41,125,1,43,131,19,45,137,139,47,143,145,49,149,151,51,155

%N a(n) = A365456(A005940(n)), where A365456(n) = A156552(2*n) / gcd(sigma(n), A156552(2*n)), and A156552 is the inverse of offset-0 version of Doudna-sequence, A005940.

%H Antti Karttunen, <a href="/A365457/b365457.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = (2*n-1) / gcd(2*n-1, A324054(n-1)).

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552

%o A365456(n) = { my(u=A156552(2*n)); (u/gcd(u, sigma(n))); };

%o A365457(n) = A365456(A005940(n));

%Y Cf. A000203, A005940, A156552, A324054, A365456.

%K nonn

%O 1,3

%A _Antti Karttunen_, Sep 10 2023