Search: id:A050376
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%I A050376
%S A050376 2,3,4,5,7,9,11,13,16,17,19,23,25,29,31,37,41,43,47,49,53,59,61,67,71,
%T A050376 73,79,81,83,89,97,101,103,107,109,113,121,127,131,137,139,149,151,157,
%U A050376 163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241
%N A050376 Numbers of the form p^(2^k) where p is prime and k >= 0.
%C A050376 Every number is a product of a unique subset of these numbers.
%C A050376 Or, a(1) = 2; for n>1, a(n) = smallest number which can not be obtained 
               as the product of previous terms. This is evident from the unique 
               factorization theorem and the fact that every number can be expressed 
               as the sum of powers of 2. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Jan 09 2002
%C A050376 Except for the first term, same as A084400. - David Wasserman (wasserma(AT)spawar.navy.mil), 
               Dec 22 2004
%C A050376 The least number having 2^n divisors (=A037992(n)) is the product of 
               the first n terms of this sequence according to Ramanujan.
%C A050376 d(n)=trivial prime (2 or 3). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Dec 01 2009]
%D A050376 S. Ramanujan, Highly Composite Numbers, Collected Papers of Srinivasa 
               Ramanujan, p. 125, Ed. G. H. Hardy et al., AMS Chelsea 2000.
%H A050376 T. D. Noe, <a href="b050376.txt">Table of n, a(n) for n=1..1000</a>
%H A050376 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Unitarism and infinitarism</
               a>.
%e A050376 6=2*3, 8=2*4, 24=2*3*4. 120 is not a member since it is divisible by 
               two different primes.
%o A050376 (PARI) {a(n)= local(m,c,k,p); if(n<=0,2*(n==0), c=0; m=2; while( c<n, 
               m++; if( isprime(m)| ( (k=ispower(m, (null),&p))&isprime(p)& k ==2^valuation(k,
               2) ), c++)); m)} /* Michael Somos Apr 15 2005 */
%Y A050376 Cf. A000040 (primes), A050377-A050380, A026416, A000028, A066724, A026477, 
               A084400.
%Y A050376 Sequence in context: A026477 A079852 A084400 this_sequence A050198 A158923 
               A008740
%Y A050376 Adjacent sequences: A050373 A050374 A050375 this_sequence A050377 A050378 
               A050379
%Y A050376 Cf. A000005 (number of divisors of n), A168546 (the nontrivial primes). 
               [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Dec 01 2009]
%K A050376 nonn,easy,nice,new
%O A050376 1,1
%A A050376 Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.

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