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A324184 a(n) = sigma(A163511(n)).

%I A324184 #13 Jul 25 2023 20:24:15
%S A324184 1,3,7,4,15,13,12,6,31,40,39,31,28,24,18,8,63,121,120,156,91,124,93,
%T A324184 57,60,78,72,48,42,32,24,12,127,364,363,781,280,624,468,400,195,403,
%U A324184 372,342,217,228,171,133,124,240,234,248,168,192,144,96,90,104,96,72,56,48,36,14,255,1093,1092,3906,847,3124,2343,2801,600
%N A324184 a(n) = sigma(A163511(n)).
%H A324184 Antti Karttunen, <a href="/A324184/b324184.txt">Table of n, a(n) for n = 0..16383</a>
%H A324184 Antti Karttunen, <a href="/A324184/a324184.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%F A324184 a(n) = A000203(A163511(n)).
%F A324184 For n >= 1, a(n) = A324054(A054429(n)).
%o A324184 (PARI) 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 A324184 (PARI)
%o A324184 A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(p+1)); n >>= 1); (t*p));
%o A324184 A324184(n) = sigma(A163511(n));
%o A324184 (Python)
%o A324184 from sympy import nextprime
%o A324184 def A324184(n):
%o A324184     if n:
%o A324184         c, p = 1, 1
%o A324184         while n:
%o A324184             c *= ((p:=nextprime(p))**(s:=(~n&n-1).bit_length()+1)-1)//(p-1)
%o A324184             n >>= s
%o A324184         return c*(p**(s+1)-1)//(p**s-1)
%o A324184     return 1 # _Chai Wah Wu_, Jul 25 2023
%Y A324184 Cf. A000203, A054429, A163511, A324054, A324183, A324185, A324186, A324187, A324188, A324189.
%K A324184 nonn
%O A324184 0,2
%A A324184 _Antti Karttunen_, Feb 17 2019