A324058 a(n) = A324121(A005940(1+n)) = gcd(A324054(n), A005940(1+n)*A106737(n)).

1, 1, 2, 1, 2, 12, 1, 1, 2, 2, 12, 4, 1, 3, 4, 1, 2, 8, 4, 6, 4, 24, 6, 12, 3, 3, 2, 1, 4, 24, 1, 3, 2, 4, 12, 56, 4, 48, 2, 10, 4, 16, 24, 24, 2, 18, 120, 4, 1, 3, 6, 1, 6, 12, 1, 3, 4, 4, 24, 8, 1, 3, 2, 1, 2, 2, 4, 12, 4, 48, 6, 8, 28, 8, 24, 112, 6, 24, 8, 2, 4, 16, 24, 336, 8, 96, 12, 120, 6, 24, 4, 6, 8, 720, 6, 36, 3, 3, 2, 21, 6, 36, 3, 15, 14, 6

Offset: 0

Author

Antti Karttunen, Feb 15 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

Crossrefs

Cf. A000005, A000203, A005940, A038040, A106737, A324054, A324057, A324121.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A106737(n) = sum(k=0, n, (binomial(n+k, n-k)*binomial(n, k)) % 2);
A324054(n) = { my(p=2,mp=p*p,m=1); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, if(3==(n%4),mp *= p,m *= (mp-1)/(p-1))); n>>=1); (m); };
A324058(n) = gcd(A324054(n), A005940(1+n)*A106737(n));
\\ Alternatively as:
A324121(n) = gcd(sigma(n),n*numdiv(n));
A324058(n) = A324121(A005940(1+n));

Formula

a(n) = A324121(A005940(1+n)) = gcd(A324054(n), A005940(1+n)*A106737(n)).