cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A324816 Binary weight of A324815; number of 1-bits in common positions in 2*A156552(n) and A323243(n).

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%I A324816 #8 Mar 17 2019 21:08:52
%S A324816 0,0,0,1,0,1,0,1,2,0,0,1,0,1,1,2,0,2,0,1,2,0,0,1,2,0,2,0,0,1,0,1,1,0,
%T A324816 2,1,0,1,1,1,0,1,0,1,2,0,0,1,2,2,1,1,0,3,2,1,1,1,0,1,0,0,2,3,1,0,0,0,
%U A324816 1,1,0,2,0,0,1,0,2,0,0,1,1,0,0,2,1,0,1,0,0,3,1,0,0,0,2,3,0,1,1,1,0,1,0,1,1
%N A324816 Binary weight of A324815; number of 1-bits in common positions in 2*A156552(n) and A323243(n).
%C A324816 Numbers 0 .. 7 occur for the first time in 1, 4, 9, 54, 162, 972, 2816, 3456. These are also the positions of records so far.
%H A324816 Antti Karttunen, <a href="/A324816/b324816.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A324816 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324816 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324816 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324816 a(n) = A000120(A324815(n)).
%F A324816 a(p) = 0 for all primes p.
%F A324816 a(A324201(n)) = A000043(n).
%o A324816 (PARI)
%o A324816 A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552 by _David A. Corneth_
%o A324816 A324816(n) = hammingweight(bitand(2*A156552(n),A323243(n))); \\ Needs code also from A323243.
%Y A324816 Cf. A000120, A156552, A323243, A324201, A324815.
%K A324816 nonn
%O A324816 1,9
%A A324816 _Antti Karttunen_, Mar 17 2019