A365432 - OEIS

%I #11 Sep 07 2023 16:11:07

%S 0,0,0,0,0,0,6,0,8,0,10,0,12,6,6,0,16,8,18,0,4,10,22,0,24,12,12,6,28,

%T 6,30,0,32,16,34,8,36,18,18,0,40,4,42,10,20,22,46,0,48,24,24,12,52,12,

%U 22,6,56,28,58,6,60,30,14,0,64,32,66,16,68,34,70,8,72,36,16,18,12,18,78,0,80,40,82,4,40,42,42,10

%N a(n) = A156552(A364502(n)), where A364502(n) = A005940(n) / gcd(n, A005940(n)), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.

%H Antti Karttunen, <a href="/A365432/b365432.txt">Table of n, a(n) for n = 1..16384</a>

%F For all n >= 1, a(n) <= n-1 and A341520(a(n), A365430(n)) = n-1.

%o (PARI)

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

%o A364502(n) = { my(u=A005940(n)); (u / gcd(n, u)); };

%o A365432(n) = A156552(A364502(n));

%Y Cf. A005940, A364500, A341520, A365430, A365431 (rgs-transform).

%K nonn

%O 1,7

%A _Antti Karttunen_, Sep 07 2023