A240667 a(n) is the GCD of the solutions x of sigma(x) = n; sigma(n) = A000203(n) = sum of divisors of n.

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

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? Answer: n = A241625(6) = 6187272.

Links

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

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

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)); }
(PARI) a(n) = my(s = invsigma(n)); if(#s, gcd(s), 0); \\ Amiram Eldar, Dec 19 2024, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000203, A007369, A007370, A211656, A241479 (a variant), A241625.

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