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A387407 Partial sums of A387422, where A387422 is the length of the maximal common prefix of the binary expansions of n and sigma(n).

%I A387407 #7 Sep 03 2025 13:11:09
%S A387407 1,2,3,4,5,8,9,10,11,13,14,16,18,20,22,23,26,30,32,36,38,40,41,43,45,
%T A387407 46,47,52,55,56,57,58,59,60,61,63,67,68,69,72,76,77,80,83,85,87,88,90,
%U A387407 92,93,94,97,101,103,104,107,108,109,112,113,117,119,121,122,124,127,131,132,133,136,139,140,145,146,147
%N A387407 Partial sums of A387422, where A387422 is the length of the maximal common prefix of the binary expansions of n and sigma(n).
%H A387407 Antti Karttunen, <a href="/A387407/b387407.txt">Table of n, a(n) for n = 1..65537</a>
%H A387407 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A387407 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A387407 a(1) = 1; and for n > 1, a(n) = a(n-1) + A387422(n).
%F A387407 a(n) = A387408(n) + A387409(n).
%o A387407 (PARI)
%o A387407 up_to = 65537;
%o A387407 A387422(n) = { my(a=binary(n), b=binary(sigma(n)), i=1); while(i<=#a,if(a[i]!=b[i],return(i-1)); i++); (#a); };
%o A387407 A387407list(up_to) = { my(v=vector(up_to)); v[1] = A387422(1); for(n=2,up_to,v[n] = v[n-1]+A387422(n)); (v); };
%o A387407 v387407 = A387407list(up_to);
%o A387407 A387407(n) = v387407[n];
%Y A387407 Cf. A003961, A387422, A387408, A387409.
%Y A387407 Cf. also A387424.
%K A387407 nonn,new
%O A387407 1,2
%A A387407 _Antti Karttunen_, Sep 03 2025