[seqfan] Is A026477 determined by prime signatures?

Charles Greathouse charles.greathouse at case.edu
Thu Aug 25 16:34:33 CEST 2016

Sequence A026477 is defined as:
a(1) = 1, a(2) = 2, a(3) = 3; and for n > 3, a(n) = smallest number >
a(n-1) and not of the form a(i)*a(j)*a(k) for 1 <= i < j < k < n.

It seems that if two numbers have the same prime signature (multiset of
prime exponents) then either both or neither are in the sequence, but I
can't prove this. Anyone? Clark? The version with two numbers (A026422) has
this property.

It's clear that all primes are in this sequence, which shows that numbers
of the form pq are not (for distinct primes p and q).

Charles Greathouse
Case Western Reserve University

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