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.
%I A080085 #29 Dec 14 2024 14:41:54
%S A080085 1,1,3,4,8,10,15,16,19,25,26,34,38,39,42,49,54,56,64,67,70,74,79,85,
%T A080085 94,97,98,102,104,109,120,128,134,135,145,146,152,159,162,168,174,176,
%U A080085 184,190,193,194,206,216,222,224,228,232,236,244,255,259,265,266,273,277
%N A080085 Number of factors of 2 in the factorial of the n-th prime, counted with multiplicity.
%C A080085 n-th prime minus number of 1's in binary representation of n-th prime. [_Juri-Stepan Gerasimov_, May 17 2010]
%H A080085 Antti Karttunen, <a href="/A080085/b080085.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)
%F A080085 a(n) = Sum_{k=1..L} floor( p_n /2^k ), where L = log(p_n)/log(2), where p_n is the n-th prime.
%F A080085 a(n) = A000040(n) - A014499(n). - _Juri-Stepan Gerasimov_, May 17 2010
%F A080085 a(n) = 1+A294898(A000040(n)). - _Antti Karttunen_, Dec 14 2024
%t A080085 lst={};Do[p=Prime[n];s=0;While[p>1,p=IntegerPart[p/2];s+=p;];AppendTo[lst,s],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 28 2009 *)
%o A080085 (PARI) vector(58, n, valuation(prime(n)!, 2)) \\ _Arkadiusz Wesolowski_, Feb 22 2014
%o A080085 (PARI) a(n) = prime(n) - hammingweight(prime(n)); \\ _Joerg Arndt_, Feb 22 2014
%Y A080085 Cf. A276133 (first differences).
%Y A080085 Cf. A000040, A080084, A080086, A080087, A294898, A371151.
%Y A080085 Column 1 of array A379008, incremented by one.
%K A080085 nonn
%O A080085 1,3
%A A080085 _Paul D. Hanna_, Jan 26 2003