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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212490 Least number m > 1 such that A000203(x)*x = m has exactly n solutions. 6
6, 336, 333312, 5418319872, 1584858562560 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

6 = 6.

336 = 6*28*2.

333312 = 6*28*496*2*2.

5418319872 = 6*28*496*8128*2*2*2.

a(6) > 5*10^14. - Michel Marcus and David A. Corneth, Nov 01 2020

From David A. Corneth, Nov 01 2020: (Start)

sigma(n)/n increases to a record in A004394. This can be used to limit the checked divisors of some candidate m.

For n >= 6, If gcd(a(4), a(5)) | a(n) then a(n) > 1.1*10^17. If (gcd(a(4), a(5)) * 2047) | a(n) then a(n) > 1.8 * 10^20. (End)

a(6) <= 6*28*496*8128*33550336*137438691328*2*2*2*2*2. - Michel Marcus, Nov 01 2020

From David A. Corneth, Nov 01 2020: (Start)

Using the same as above, a(7) <= 1716908124551996896669734276042690920448.

a(8) <= 7917841189233800244470292555938612387093638081493952626688. (End)

Conjecture: a(n) <= 2^(n-1) * Product_{k=1..n} A000396(k). - Daniel Suteu, Nov 01 2020

From Daniel Suteu, Nov 01 2020: (Start)

a(6) <= 7089671638182002688000,

a(7) <= 106345074572730040320,

a(9) <= 1826980530660612389572800675840. (End)

REFERENCES

R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third Edition, 2004, B11.

LINKS

Table of n, a(n) for n=1..5.

David A. Corneth, Pari program

EXAMPLE

For n=3, 333312 has exactly 3 solutions: sigma(434)*434 = 333312, sigma(372)*372 = 333312, and sigma(336)*336 = 333312; therefore a(3) = 333312.

PROG

(PARI) isok(k, n) = sumdiv(k, d, d*sigma(d) == k) == n;

a(n) = my(k=2); while (! isok(k, n), k++); k; \\ Michel Marcus, Oct 28 2020

(PARI) See Corneth link \\ David A. Corneth, Nov 01 2020

CROSSREFS

Cf. A000203, A004394, A212489, A212327, A212373.

Sequence in context: A210769 A003031 A144849 * A047941 A229501 A289738

Adjacent sequences:  A212487 A212488 A212489 * A212491 A212492 A212493

KEYWORD

nonn,more

AUTHOR

Naohiro Nomoto, May 18 2012

EXTENSIONS

a(5) from Donovan Johnson, May 20 2012

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 November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)