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A325608
Numbers whose factorization into factors prime(i)/i does not have weakly decreasing nonzero multiplicities.
2
147, 245, 294, 357, 490, 511, 539, 588, 595, 637, 681, 714, 735, 845, 847, 853, 867, 903, 980, 1022, 1029, 1043, 1078, 1083, 1135, 1176, 1183, 1190, 1239, 1241, 1267, 1274, 1309, 1362, 1421, 1428, 1445, 1470, 1505, 1519, 1547, 1553, 1563, 1617, 1631, 1690
OFFSET
1,1
COMMENTS
Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example, 147 = q(1)^5 q(2) q(4)^2 has multiplicities (5,1,2), which are not weakly decreasing, so 147 belongs to the sequence.
MATHEMATICA
difac[n_]:=If[n==1, {}, With[{i=PrimePi[FactorInteger[n][[1, 1]]]}, Sort[Prepend[difac[n*i/Prime[i]], i]]]];
Select[Range[1000], !GreaterEqual@@Length/@Split[difac[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 12 2019
STATUS
approved