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A074391
a(n) is the smallest number such that gcd(a(n), sigma(a(n))) = n.
3
1, 10, 15, 12, 95, 6, 91, 56, 153, 40, 473, 24, 117, 182, 135, 336, 1139, 90, 703, 380, 861, 946, 3151, 168, 3725, 468, 1431, 28, 5017, 570, 775, 992, 891, 2176, 4865, 792, 2701, 1406, 585, 280, 6683, 546, 11051, 1892, 1305, 6302, 13207, 528, 4753, 5800
OFFSET
1,2
COMMENTS
a(n) is the smallest number k such that A017666(k), the denominator of sigma(k)/k, is equal to k/n. - Jaroslav Krizek, Sep 23 2014
Each term a(n) is divisible by its index n. - Michel Marcus, Jan 13 2015
LINKS
FORMULA
a(n) = Min{x; gcd(x, sigma(x))} = Min{x; gcd(x, A000203(x))} = n. - corrected by Michel Marcus, Jan 13 2015
EXAMPLE
n=6: a(6)=6 because gcd(6, sigma(6))=6 and a(6)=6 is the smallest.
MAPLE
f:= proc(n) local k;
for k from n by n do
if igcd(k, numtheory:-sigma(k))=n then return k fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Feb 11 2020
MATHEMATICA
f[x_] := GCD[DivisorSigma[1, x], x] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}];
PROG
(Magma) A074391:=func<n|exists(r){k: k in[1..1000000] | Denominator(SumOfDivisors(k)/k) eq k/n}select r else-1>; [A074391(n): n in[1..100]] // Jaroslav Krizek, Sep 23 2014
(PARI) a(n) = my(k=1); while (gcd(sigma(k), k) != n, k++); k; \\ Michel Marcus, Jan 13 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 23 2002
STATUS
approved