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!)
A248029 Least positive integer m such that m + n divides phi(m)*sigma(n), where phi(.) and sigma(.) are given by A000010 and A000203. 3
1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 2, 1, 10, 9, 15, 1, 8, 1, 1, 11, 14, 1, 6, 6, 16, 5, 14, 1, 6, 1, 10, 15, 11, 13, 16, 1, 7, 9, 5, 1, 6, 1, 12, 7, 26, 1, 14, 8, 12, 21, 46, 1, 6, 17, 4, 23, 32, 1, 24, 1, 34, 41, 63, 7, 6, 1, 16, 11, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

Conjecture: For any n > 1, we have a(n) <= n.

The existence of a(n) is easy; in fact, for m = sigma(n) - n, obviously m + n divides phi(m)*sigma(n). - Zhi-Wei Sun, Oct 02 2014

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 2..10000

Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

EXAMPLE

a(8) = 7 since 7 + 8 = 15 divides phi(7)*sigma(8) = 6*15 = 90.

MATHEMATICA

Do[m=1; Label[aa]; If[Mod[EulerPhi[m]*DivisorSigma[1, n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 2, 70}]

PROG

(PARI)

a(n)=m=1; while((eulerphi(m)*sigma(n))%(m+n), m++); m

vector(100, n, a(n)) \\ Derek Orr, Sep 29 2014

CROSSREFS

Cf. A000010, A000203, A248004, A248007, A248008, A248030.

Sequence in context: A193279 A076889 A134689 * A117552 A294886 A069250

Adjacent sequences:  A248026 A248027 A248028 * A248030 A248031 A248032

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Sep 29 2014

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 October 18 06:50 EDT 2021. Contains 348066 sequences. (Running on oeis4.)