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a(n) = A003415(A019565(n)).
3

%I #16 Apr 09 2021 09:22:18

%S 0,1,1,5,1,7,8,31,1,9,10,41,12,59,71,247,1,13,14,61,16,87,103,371,18,

%T 113,131,493,167,719,886,2927,1,15,16,71,18,101,119,433,20,131,151,

%U 575,191,837,1028,3421,24,191,215,859,263,1241,1504,5153,311,1623,1934,6871,2556,10117,12673,40361,1,19,20,91,22,129

%N a(n) = A003415(A019565(n)).

%H Antti Karttunen, <a href="/A342921/b342921.txt">Table of n, a(n) for n = 0..8192</a>

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

%F a(n) = A003415(A019565(n)) = A069359(A019565(n)).

%F a(n) = A327860(A276156(n)) = A329029(A276156(n)) = A342002(A276156(n)).

%t Array[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]] &, 70, 0] (* _Michael De Vlieger_, Apr 08 2021 *)

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o A342921(n) = A003415(A019565(n));

%Y Cf. A003415, A019565, A069359, A276156, A327860, A329029, A342002.

%K nonn,look

%O 0,4

%A _Antti Karttunen_, Apr 06 2021