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%I #21 Jul 27 2023 11:00:19
%S 1,1,2,1,2,4,2,1,1,2,2,2,2,4,4,1,2,3,2,6,4,4,2,4,1,2,4,2,2,8,2,3,4,2,
%T 4,1,2,4,4,2,2,8,2,6,6,4,2,2,3,3,4,2,2,8,4,8,4,2,2,12,2,4,2,1,4,8,2,6,
%U 4,8,2,3,2,2,2,2,4,8,2,2,1,2,2,4,4,4,4,4,2,6,4,6,4,4,4,12,2,3,6,1,2,8,2,2,8,2,2,4,2,8,4,2,2,8,4,6,2,4,4,8
%N a(n) = gcd(d(n), sigma(n)).
%H Antti Karttunen, <a href="/A009205/b009205.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[GCD[DivisorSigma[0,n],DivisorSigma[1,n]],{n,120}] (* _Harvey P. Dale_, Dec 05 2017 *)
%o (PARI) A009205(n) = gcd(numdiv(n),sigma(n)); \\ _Antti Karttunen_, May 22 2017
%o (Python)
%o from math import prod, gcd
%o from sympy import factorint
%o def A009205(n):
%o f = factorint(n).items()
%o return gcd(prod(e+1 for p, e in f),prod((p**(e+1)-1)//(p-1) for p,e in f)) # _Chai Wah Wu_, Jul 27 2023
%Y Cf. A000005, A000203, A009191, A009194, A087801, A286360.
%K nonn
%O 1,3
%A _David W. Wilson_
%E Data section extended to 120 terms by _Antti Karttunen_, May 22 2017
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