[seqfan] Smallest number not of the form a(i)*a(j)*a(k) for 1 <= i < j < k < n

Charles Greathouse charles.greathouse at case.edu
Thu Sep 17 05:00:20 CEST 2015


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 there should be a succinct description for this sequence in
terms of the exponents appearing in the prime factorization of n (such as
there is for A026422). Can any prove or disprove this claim?

It's clear that every prime appears, as does every square of a prime, but
that no cubes of primes can appear. By induction p^e appears with e in (0,
1, 2, 4, 8, 15, 22, 29, ...) =~ A026474, a linear recurrence.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


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