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a(n) = A106315(A163511(n)).
7

%I #9 Feb 19 2019 00:10:49

%S 0,1,5,2,2,1,0,4,18,28,30,13,16,12,4,6,3,42,72,32,51,78,21,33,12,36,

%T 24,44,36,20,8,10,67,2,168,1,176,504,128,172,84,10,312,102,32,198,75,

%U 97,108,120,144,58,48,72,128,20,50,66,48,4,0,36,16,12,4,731,372,3126,625,6,785,801,456,1332,768,1720,540,232,688,932,145,660

%N a(n) = A106315(A163511(n)).

%H Antti Karttunen, <a href="/A324187/b324187.txt">Table of n, a(n) for n = 0..16384</a>

%H Antti Karttunen, <a href="/A324187/a324187.txt">Data supplement: n, a(n) computed for n = 0..65537</a>

%F a(n) = A106315(A163511(n)) = (A163511(n)*A324183(n)) mod A324184(n).

%F For n > 0, a(n) = A324057(A054429(n)).

%o (PARI)

%o A106315(n) = (n*numdiv(n) % sigma(n));

%o 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));

%o A324187(n) = A106315(A163511(n));

%o (PARI)

%o 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)));

%o 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)));

%o A324187(n) = ((A163511(n)*A324183(n))%A324184(n));

%Y Cf. A054429, A106315, A163511, A324057, A324183, A324184, A324188, A324189.

%Y Cf. A324199 (positions of zeros).

%K nonn

%O 0,3

%A _Antti Karttunen_, Feb 17 2019