

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
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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] (* JeanFrançois 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



