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A325608 Numbers whose factorization into factors prime(i)/i does not have weakly decreasing nonzero multiplicities. 2

%I

%S 147,245,294,357,490,511,539,588,595,637,681,714,735,845,847,853,867,

%T 903,980,1022,1029,1043,1078,1083,1135,1176,1183,1190,1239,1241,1267,

%U 1274,1309,1362,1421,1428,1445,1470,1505,1519,1547,1553,1563,1617,1631,1690

%N Numbers whose factorization into factors prime(i)/i does not have weakly decreasing nonzero multiplicities.

%C 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.

%t difac[n_]:=If[n==1,{},With[{i=PrimePi[FactorInteger[n][[1,1]]]},Sort[Prepend[difac[n*i/Prime[i]],i]]]];

%t Select[Range[1000],!GreaterEqual@@Length/@Split[difac[#]]&]

%Y Cf. A001222, A056239, A112798, A118914.

%Y Matula-Goebel numbers: A007097, A061775, A109129, A196050, A317713, A324935.

%Y q-factorization: A324922, A324923, A324924, A324931, A325613, A325614, A325615, A325660, A325662.

%K nonn

%O 1,1

%A _Gus Wiseman_, May 12 2019

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Last modified April 11 18:59 EDT 2021. Contains 342888 sequences. (Running on oeis4.)