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!)
A240667 a(n) is the GCD of the solutions x of sigma(x) = n; sigma(n) = A000203(n) = sum of divisors of n. 8
1, 0, 2, 3, 0, 5, 4, 7, 0, 0, 0, 1, 9, 13, 8, 0, 0, 1, 0, 19, 0, 0, 0, 1, 0, 0, 0, 12, 0, 29, 1, 1, 0, 0, 0, 22, 0, 37, 18, 27, 0, 1, 0, 43, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 49, 0, 0, 1, 0, 61, 32, 0, 0, 0, 0, 67, 0, 0, 0, 1, 0, 73, 0, 0, 0, 45, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

From n=1 to 5, the least integers such that a(x)=n, depending on if singletons (see A007370 and A211656) are accepted or not, are 1, 3, 4, 7, 6 or 12, 126, 124, 210, 22152.

Is it possible to find an integer n such that a(n) = 6?

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(A007369(n)) = 0.

EXAMPLE

There are no integers such that sigma(x)=2, so a(2)=0.

There is a single integer, x=2, such that sigma(x)=3, so a(3)=2.

There are 2 integers, x=6 and 11, such that sigma(x)=12, their gcd is 1, so a(12)=1.

MAPLE

A240667 := n -> igcd(op(select(k->sigma(k)=n, [$1..n]))):

seq(A240667(n), n=1..82); # Peter Luschny, Apr 13 2014

MATHEMATICA

a[n_] := GCD @@ Select[Range[n], DivisorSigma[1, #] == n&];

Array[a, 100] (* Jean-François Alcover, Jul 30 2018 *)

PROG

(PARI) sigv(n) =  select(i->sigma(i) == n, vector(n, i, i));

a(n) = {v = sigv(n); if (#v == 0, 0, gcd(v)); }

CROSSREFS

Cf. A000203, A007369, A007370, A211656, A241479 (a variant).

Sequence in context: A277516 A322333 A346615 * A051444 A299762 A057637

Adjacent sequences:  A240664 A240665 A240666 * A240668 A240669 A240670

KEYWORD

nonn

AUTHOR

Michel Marcus, Apr 10 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 December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)