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%I #14 Jul 31 2016 17:33:31
%S 1,2,4,8,15,16,30,32,60,64,77,120,128,154,221,225,240,256,308,437,442,
%T 450,480,512,616,874,884,899,900,960,1024,1155,1232,1517,1748,1768,
%U 1798,1800,1920,2021,2048,2310,2464,3034,3127,3315,3375,3496,3536,3596,3600
%N Numbers n for which e_n(2*i)=e_n(2*i+1), for all i>=1, where e_n(k)>=0 denote the exponent of prime(k) in the prime power representation of n.
%C There exists a permutation alpha of the sequence such that {alpha(a(n))} is a completely multiplicative function.
%C Numbers which are the product of zero or more of {2, 3*5, 7*11, 13*17, 19*23, ...} with multiplicity. - _Charles R Greathouse IV_, Jul 30 2016
%H Charles R Greathouse IV, <a href="/A275474/b275474.txt">Table of n, a(n) for n = 1..10000</a>
%e 1 is a member, since all e_1(k)=0;
%e Powers 2^m, m>=1, are members, since e_2^m(k)=0, for all k>=2;
%e 15 is a member, since e_15(2)*e_15(3)=1;
%e n = 2983500 is a member, since e_n(1)=2, e_n(2)=e_n(3)=3 and e_n(6)=e_n(7)=1, all other e_n(k)=0.
%o (PARI) is(n)=my(f=factor(n>>valuation(n,2))); if (#f~%2, return(0)); for(i=1,#f~/2, if(f[2*i-1,2]!=f[2*i,2] || nextprime(f[2*i-1,1]+1)!=f[2*i,1], return(0))); for(i=1,#f~/2, if(primepi(f[2*i,1])%2==0, return(0))); 1 \\ _Charles R Greathouse IV_, Jul 30 2016
%o (PARI) list(lim)=my(v=List([1,2]),p=3,pStart=2,pEnd,start=2,end,nStart,t); lim\=1; forprime(q=5,sqrtint(lim+1)+1, p=if(p, listput(v,p*q); 0, q)); end=pEnd=#v; for(n=2,logint(lim,2), nStart=end+1; for(i=start,end, for(j=pStart,pEnd, t=v[i]*v[j]; if(t>lim, break); listput(v, t))); start=nStart; end=#v); Set(v) \\ _Charles R Greathouse IV_, Jul 30 2016
%Y Cf. A000040, A001248, A089581, A275246, A275248, A275249, A275251, A275252, A275253, A275407.
%K nonn
%O 1,2
%A _Vladimir Shevelev_, Jul 29 2016
%E More terms from _Peter J. C. Moses_, Jul 29 2016
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