A324189 a(n) = A324122(A163511(n)).

0, 2, 6, 2, 14, 12, 0, 4, 30, 36, 36, 30, 24, 12, 16, 6, 60, 120, 96, 152, 90, 122, 90, 54, 48, 72, 48, 44, 36, 28, 16, 10, 126, 362, 360, 780, 272, 600, 464, 396, 192, 402, 360, 336, 216, 222, 168, 132, 120, 120, 216, 246, 144, 168, 128, 92, 80, 102, 48, 68, 0, 36, 32, 12, 254, 1092, 1080, 3900, 846, 3122, 2342, 2800, 576, 2016, 1824, 2360, 1080

Offset: 0

Author

Antti Karttunen, Feb 17 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Crossrefs

Cf. A163511, A324183, A324184, A324188.

Cf. A324199 (positions of zeros).

Programs

PARI

A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A324122(n) = (sigma(n) - gcd(sigma(n),n*numdiv(n)));
A324189(n) = A324122(A163511(n));

PARI

A324183(n) = if(!n,1,n = ((3<<#binary(n\2))-n-1); my(e=0,m=1); while(n>0, if(!(n%2), m *= (1+e); e=0, e++); n >>= 1); (m*(1+e)));
A324184(n) = if(!n,1,my(p=2,mp=p*p,m=1); while(n>1, if(n%2, p=nextprime(1+p); mp = p*p, if((2==n)||!(n%4),mp *= p,m *= (mp-1)/(p-1))); n >>= 1); (m*(mp-1)/(p-1)));
A324189(n) = (A324184(n) - gcd(A324184(n), A163511(n)*A324183(n)));

Formula

a(n) = A324184(n) - A324188(n) = A324184(n) - gcd(A324184(n),A163511(n)*A324183(n)).