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!)
A246827 Smallest x such that sigma(x)/x = 2*sigma(n)/n where sigma(n) is the sum of divisors of n. 1
6, 120, 84, 4320, 30, 30240, 42, 293760, 252, 3360, 66, 208565280, 78, 840, 420, 760320, 102, 18506880, 114, 131040, 1890, 1320, 138, 14182439040, 150, 1560, 756, 30240, 174, 668304000, 186, 1272960, 924, 2040, 210, 2068967577600, 222, 2280, 1092, 8910720, 246 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

When n is odd, and if there are infinitely many Mersenne primes, then a(n) would be at most equal to n multiplied by the smallest perfect number (A000396) whose prime Mersenne component (A000668) is coprime to n.

When n is even, there is no such obvious upper bound.

Conjecture: a(n) exists for all n.

It appears that a(n) is divisible by n.

LINKS

Michel Marcus, Table of n, a(n) for n = 1..500

M. Kozek, F. Luca, P. Pollack, and C. Pomerance, Harmonious pairs, p. 16, 20, IJNT, to appear.

Michel Marcus, solveBA PARI script

P. Pollack and C. Pomerance, Some problems of Erdős on the sum-of-divisors function, (2015), p. 17, 22.

P. Pollack, C. Pomerance, Some problems of Erdos on the sum-of-divisors function, For Richard Guy on his 99th birthday: May his sequence be unbounded, 2015, to appear.

PROG

(PARI) a(n) =  {nv = 2*sigma(n)/n; lim = 1; sv = []; while (#sv == 0, lim *= 10^10; sv = vecsort(solveBA(numerator(nv), denominator(nv), lim))); return (sv[1]); }

CROSSREFS

Cf. A000203, A000396, A000668, A017665, A017666.

Sequence in context: A054957 A271648 A290341 * A127726 A117063 A178911

Adjacent sequences:  A246824 A246825 A246826 * A246828 A246829 A246830

KEYWORD

nonn

AUTHOR

Michel Marcus, Sep 04 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 March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)