Search: id:A003958
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%I A003958
%S A003958 1,1,2,1,4,2,6,1,4,4,10,2,12,6,8,1,16,4,18,4,12,10,22,2,16,12,8,6,28,8,
%T A003958 30,1,20,16,24,4,36,18,24,4,40,12,42,10,16,22,46,2,36,16,32,12,52,8,40,
               6,
%U A003958 36,28,58,8,60,30,24,1,48,20,66,16,44,24,70,4,72,36,32,18,60,24,78,4,16
%N A003958 If n = Product p(k)^e(k) then a(n) = Product (p(k)-1)^e(k), a(1) = 1.
%C A003958 Completely multiplicative.
%C A003958 a(n) = A000010(n) iff n is square-free (see A005117). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Nov 05 2004
%H A003958 Daniel Forgues, <a href="b003958.txt">Table of n, a(n) for n=1..100000</
               a>
%F A003958 If n = Product p(k)^e(k) then a(n) = Product (p(k)-1)^e(k), a(1) = 1.
%F A003958 Multiplicative with a(p^e) = (p-1)^e. - David W. Wilson (davidwwilson(AT)comcast.net), 
               Aug 01, 2001.
%o A003958 (PARI) a(n)=if(n<1,0,direuler(p=2,n,1/(1-p*X+X))[n]) (from R. Stephan)
%Y A003958 Cf. A003959.
%Y A003958 Adjacent sequences: A003955 A003956 A003957 this_sequence A003959 A003960 
               A003961
%Y A003958 Cf. A168065, A168066. [From Daniel Forgues (squid(AT)zensearch.com), 
               Dec 01 2009]
%K A003958 nonn,mult,nice
%O A003958 1,3
%A A003958 Marc LeBrun (mlb(AT)well.com)
%E A003958 Definition reedited (from formula) by Daniel Forgues (squid(AT)zensearch.com), 
               Nov 17 2009

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