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A348123
Starts of runs of 3 consecutive numbers that have more nonunitary than unitary prime divisors (A348121).
1
959075, 1492775, 5038523, 5132699, 9905300, 38002831, 40441023, 50473575, 67706631, 80108775, 81355923, 109436875, 128428999, 165332223, 169067491, 171024111, 178878175, 196224075, 224042624, 247529574, 274205223, 279645399, 282880575, 284267374, 299969423, 329523775
OFFSET
1,1
COMMENTS
There are no runs of 4 consecutive numbers below 2.4*10^10.
It is conjectured that there are no runs of 3 consecutive numbers that are powerful (A001694), but if they do exist, their starts are contained in this sequence.
LINKS
EXAMPLE
959075 is a term since 959075 = 5^2 * 13^2 * 227, 959075 + 1 = 959076 = 2^2 * 3^2 * 26641 and 959075 + 2 = 959077 = 7^2 * 23^2 * 37 all have 2 nonunitary prime divisors and only 1 unitary prime divisor.
MATHEMATICA
q[n_] := 2*Count[(e = FactorInteger[n][[;; , 2]]), 1] < Length[e]; v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 2]], {k, 4, 5*10^7}]; seq
CROSSREFS
Subsequence of A348121 and A348122.
Cf. A001694.
Similar sequence: A348120.
Sequence in context: A341897 A341898 A092377 * A022236 A083609 A093216
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 01 2021
STATUS
approved