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

1,2

Comments

Every prime occurs in the sequence.

Links

Table of n, a(n) for n=1..60.

Prog

(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

Crossrefs

Cf. A066720, A260873.

Sequence in context: A026410 A066720 A079851 * A060634 A279457 A359891

Adjacent sequences: A381060 A381061 A381062 * A381064 A381065 A381066

Keyword

nonn

Author

Neal Gersh Tolunsky, Feb 12 2025

Extensions

More terms from Jinyuan Wang, Feb 13 2025

Status

approved