A324906 - OEIS

%I #15 Jul 10 2022 13:23:38

%S 2,3,0,4,0,0,0,5,5,0,0,0,0,0,0,6,0,3,0,0,0,0,0,0,6,0,0,0,0,0,0,7,0,0,

%T 0,2,0,0,0,0,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,

%U 0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,1,0,0,0,0,0

%N Number of trailing 1-bits in the binary representation of A318466(n), where A318466(n) = 2*n OR sigma(n).

%H Antti Karttunen, <a href="/A324906/b324906.txt">Table of n, a(n) for n = 1..65537</a>

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A007814(1+A318466(n)).

%t Array[LengthWhile[Reverse@ IntegerDigits[BitOr[2 #, DivisorSigma[1, #]], 2], # == 1 &] &, 105] (* _Michael De Vlieger_, Mar 30 2019 *)

%o (PARI)

%o A318466(n) = bitor(2*n, sigma(n));

%o A324906(n) = valuation(1+A318466(n),2);

%o (Python)

%o from sympy import divisor_sigma

%o def A324906(n): return ((m:=(n<<1)|int(divisor_sigma(n)))&~(m+1)).bit_length() # _Chai Wah Wu_, Jul 10 2022

%Y Cf. A000203, A003986, A007814, A318466, A324904, A324908.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 28 2019