A324180 - OEIS

%I #7 Feb 19 2019 18:19:56

%S 0,0,0,1,0,3,0,3,2,5,0,3,0,9,6,7,0,5,0,3,10,17,0,3,4,33,6,3,0,5,0,15,

%T 18,65,12,7,0,129,34,15,0,9,0,3,6,257,0,3,8,9,66,3,0,9,20,23,130,513,

%U 0,15,0,1025,6,31,36,17,0,3,258,9,0,3,0,2049,10,3,24,33,0,23,14,4097,0,23,68,8193,514,39,0,9,40,3

%N SumXOR variant of A297168.

%H Antti Karttunen, <a href="/A324180/b324180.txt">Table of n, a(n) for n = 1..4096</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = Cumulative XOR of A297112(d), where d ranges over the proper divisors d of n.

%o (PARI)

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

%o A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));

%o A297112(n) = if(1==n, 0, 2^A297167(n));

%o A324180(n) = { my(v=0); fordiv(n, d, if(d<n, v = bitxor(v,A297112(d)))); (v); };

%Y Cf. A061395, A156552, A297106, A297112, A297167, A297168, A324181 (rgs-transform), A324120 (number of 1-bits).

%K nonn

%O 1,6

%A _Antti Karttunen_, Feb 19 2019