login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 * A255103 A184542 A162701

Adjacent sequences:  A325605 A325606 A325607 * A325609 A325610 A325611

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 12 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)