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A378518 a(n) = n - A019565(A048675(n)), where A019565 and A048675 are base-2 exp and log-functions.

%I A378518 #11 Nov 29 2024 21:04:32
%S A378518 0,0,0,1,0,0,0,2,4,0,0,7,0,0,0,11,0,8,0,5,0,0,0,14,18,0,12,7,0,0,0,22,
%T A378518 0,0,0,21,0,0,0,10,0,0,0,11,38,0,0,33,38,36,0,13,0,24,0,14,0,0,0,53,0,
%U A378518 0,28,49,0,0,0,17,0,0,0,42,0,0,54,19,0,0,0,73,74,0,0,49,0,0,0,22,0,76,0,23,0,0,0,66,0,76
%N A378518 a(n) = n - A019565(A048675(n)), where A019565 and A048675 are base-2 exp and log-functions.
%C A378518 No negative terms because A097246(n) <= n for all n.
%H A378518 Antti Karttunen, <a href="/A378518/b378518.txt">Table of n, a(n) for n = 1..20000</a>
%F A378518 a(n) = n - A097248(n).
%o A378518 (PARI)
%o A378518 A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i, 1]+1)^(f[i, 2]\2))*((f[i, 1])^(f[i, 2]%2))); };
%o A378518 A097248(n) = { my(k=A097246(n)); while(k<>n, n = k; k = A097246(k)); k; };
%o A378518 A378518(n) = (n - A097248(n));
%Y A378518 Cf. A005117 (positions of 0's), A019565, A048675, A097246, A097248, A376406.
%Y A378518 Cf. also A376417, A376418 (analogous sequences for other bases than base-2).
%K A378518 nonn
%O A378518 1,8
%A A378518 _Antti Karttunen_, Nov 29 2024