A381063 Lexicographically earliest sequence of positive integers such that each nonempty subset has a distinct geometric mean.
1, 2, 3, 5, 7, 8, 11, 13, 17, 18, 19, 23, 29, 31, 37, 41, 43, 47, 50, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 98, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 176, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251
Offset: 1
Keywords
Programs
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PARI
is(v, w, k) = my(f=factor(k), x, y, z); for(i=1, #f~, if(setsearch(v, f[i, 1]), listput(w, f[i, 1]))); w=Set(w); forsubset(#w, r, x=#r; y=k*prod(i=1, x, w[r[i]]); forsubset(#w, s, z=#s; if(y^z==prod(i=1, z, w[s[i]])^(x+1)&&z>0, return(0)))); 1; lista(nn) = my(f, k=1, v=[1], w=List([1])); for(n=2, nn, while(!isprime(k++), if(is(v, w, k), f=factor(k); for(i=1, #f~, if(setsearch(v, f[i, 1]), listput(w, f[i, 1]))); listput(w, k); break)); v=concat(v, k)); v; \\ Jinyuan Wang, Feb 13 2025
Extensions
More terms from Jinyuan Wang, Feb 13 2025
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