A324394 a(n) = A009194(A005940(1+n)), where A005940 is the Doudna sequence and A009194(n) = gcd(n,sigma(n)).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 3, 4, 1, 3, 1, 1, 1, 2, 1, 2, 1, 6, 3, 12, 1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 3, 28, 1, 6, 1, 10, 1, 2, 3, 12, 1, 18, 15, 4, 1, 1, 3, 1, 1, 6, 1, 3, 1, 2, 3, 4, 1, 3, 1, 1, 1, 2, 1, 4, 1, 6, 3, 8, 7, 2, 3, 28, 1, 6, 1, 2, 1, 2, 3, 28, 1, 6, 3, 120, 1, 2, 1, 6, 1, 90, 3, 12, 1, 1, 1, 7, 1, 6, 3, 5, 7, 2

Offset: 0

Author

Antti Karttunen, Mar 05 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A009194, A324054, A324055, A324058, A324349, A324395.

Programs

PARI

A324394(n) = { my(m1=1,m2=1,p=2,mp=p*p); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, m1 *= p; if(3==(n%4),mp *= p,m2 *= (mp-1)/(p-1))); n>>=1); gcd(m1,m2); };

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A009194(n) = gcd(n, sigma(n));
A324394(n) = A009194(A005940(1+n));

Formula

a(n) = A009194(A005940(1+n)) = gcd(A005940(1+n), A324054(n)).