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

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.

Links

Table of n, a(n) for n=1..46.

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

Cf. A001222, A056239, A112798, A118914.

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

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

Sequence in context: A122064 A320511 A259288 * A375155 A255103 A184542

Adjacent sequences: A325605 A325606 A325607 * A325609 A325610 A325611

Keyword

nonn

Author

Gus Wiseman, May 12 2019

Status

approved