login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A337045 Indecomposable sigma-powerful numbers: powerful numbers k such that sigma(k) is also powerful, but restricted to terms that are not the product of 2 terms > 1 of A337044. 4
81, 343, 400, 9261, 189728, 224939, 972000, 1705636, 2205472, 3087000, 3591200, 3648100, 7968032, 13645088, 15350724, 21161304, 24240600, 25992000, 26680500, 29184800, 32832900, 48586824, 51595489, 80802000, 103617387, 109215352, 110215125, 119604096, 122805792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is an implementation of the suggestion that Walter A. Kehowski made on his website (see link) with regard to so-called indecomposable sigma-powerful numbers. However, the results deviate from the table linked there. The table is considered to be deficient.

LINKS

David A. Corneth, Table of n, a(n) for n = 1..6421 (terms < 10^18)

Walter A. Kehowski, Sigma-powerful numbers, Aug 09 2010.

EXAMPLE

From David A. Corneth, Aug 29 2020: (Start)

No two proper divisors of 400 are sigma-powerful and have the product of those divisors 400 so 400 is in the sequence.

27783 = 81 * 343 is sigma-powerful but 81 and 343 are sigma-powerful as well so 27783 can be decomposed into two sigma-powerful factors. So 27783 is not in the sequence. (End)

PROG

(PARI) v=vector(50); n=0;

for(m=2, 150000000, my(is); if(ispowerful(m) && ispowerful(sigma(m)), v[n++]=m; is=1; for(j=1, n-1, if(v[n]%v[j], , if(vecsearch(v[1..n-1], v[n]/v[j]), is=0; break))); if(is, print1(v[n], ", "))))

CROSSREFS

Cf. A000203, A001694, A128607, A180090, A337044.

Sequence in context: A238039 A232284 A337044 * A128607 A180090 A217967

Adjacent sequences:  A337042 A337043 A337044 * A337046 A337047 A337048

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Aug 15 2020

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 7 12:59 EDT 2022. Contains 355989 sequences. (Running on oeis4.)