cp's OEIS Frontend

A323167 a(n) = A294898(A122111(n)).

%I A323167 #7 Jan 11 2019 20:35:41
%S A323167 0,0,0,0,0,-2,0,2,3,-6,0,0,0,-14,-5,3,0,2,0,-4,-21,-30,0,1,10,-62,16,
%T A323167 -12,0,-16,0,7,-53,-126,-16,7,0,-254,-117,-3,0,-52,0,-28,4,-510,0,5,
%U A323167 38,8,-245,-60,0,19,-68,-11,-501,-1022,0,-15,0,-2046,-20,9,-172,-124,0,-124,-1013,-58,0,16,0,-4094,22,-252,-42,-268,0,1,38
%N A323167 a(n) = A294898(A122111(n)).
%H A323167 Antti Karttunen, <a href="/A323167/b323167.txt">Table of n, a(n) for n = 1..12000</a>
%H A323167 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A323167 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A323167 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A323167 a(n) = A294898(A122111(n)).
%F A323167 a(n) = A323174(n) - A322867(n).
%o A323167 (PARI)
%o A323167 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A323167 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A323167 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A323167 A294898(n) = (A005187(n)-sigma(n));
%o A323167 A323167(n) = A294898(A122111(n));
%o A323167 \\ Or alternatively as:
%o A323167 A322867(n) = hammingweight(A122111(n));
%o A323167 A323174(n) = { my(k=A122111(n)); ((2*k)-sigma(k)); }
%o A323167 A323167(n) = (A323174(n) - A322867(n));
%Y A323167 Cf. A000203, A005187, A294898, A122111, A322867, A323174, A323168.
%Y A323167 Cf. also A295296, A323248.
%K A323167 sign
%O A323167 1,6
%A A323167 _Antti Karttunen_, Jan 10 2019