OFFSET
1,2
COMMENTS
Also numbers k such that the minima of the maximal anti-runs in the weakly increasing sequence of prime factors of k (with multiplicity) are identical. Here, an anti-run is a sequence with no adjacent equal parts, and the minima of the maximal anti-runs in a sequence are obtained by splitting it into maximal anti-run subsequences and taking the least term of each. Note the prime factors can alternatively be taken in weakly decreasing order.
The complement is a superset of A036785 = products of a squarefree number and a prime power.
The asymptotic density of this sequence is (1/zeta(2)) * (1 + Sum_{p prime} (1/(p^2-p)) / Product_{primes q <= p} (1 + 1/q) = 0.884855661165... . - Amiram Eldar, Oct 26 2024
LINKS
EXAMPLE
The prime factors of 300 are {2,2,3,5,5}, with maximal anti-runs {{2},{2,3,5},{5}}, with minima (2,2,5), so 300 is not in the sequence.
MATHEMATICA
Select[Range[100], SameQ@@Min /@ Split[Flatten[ConstantArray@@@FactorInteger[#]], UnsameQ]&]
PROG
(PARI) is(k) = if(k > 1, my(e = factor(k)[, 2]); vecprod(e) == e[1], 1); \\ Amiram Eldar, Oct 26 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Gus Wiseman, Aug 16 2024
STATUS
approved