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A318781 A188999(m)/m for the integers m such that A188999(m) is divisible by m, where A188999 is the bi-unitary sigma function.

%I A318781 #19 Sep 07 2018 08:33:18
%S A318781 1,2,2,2,3,3,3,3,3,4,3,3,4,3,4,3,4,3,3,4,4,3,3,3,4,4,4,3,3,4,3,4,4,3,
%T A318781 4,3,3,4,4,4,4,3
%N A318781 A188999(m)/m for the integers m such that A188999(m) is divisible by m, where A188999 is the bi-unitary sigma function.
%C A318781 10496266260480 is a term of A189000 and it is the smallest known value x such that A188999(x)/x is 5.
%F A318781 a(n) = A188999(A189000(n))/A189000(n).
%o A318781 (PARI) a188999(n) = my(f = factor(n)); for (i=1, #f~, p = f[i, 1]; e = f[i, 2]; f[i, 1] = if (e % 2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)); f[i, 2] = 1; ); factorback(f) \\ after _Michel Marcus_ in A189000
%o A318781 is_a189000(n) = ! frac(a188999(n)/n) \\ after _Michel Marcus_ in A189000
%o A318781 for(n=1, oo, if(is_a189000(n), print1(a188999(n)/n, ", "))) \\ _Felix Fröhlich_, Sep 03 2018
%Y A318781 Cf. A188999 (bi-unitary sigma), A189000 (multiply perfect for bi-unitary sigma).
%Y A318781 Cf. A054030 (analog for sigma), A007691 (multiply perfect for sigma).
%K A318781 nonn,more
%O A318781 1,2
%A A318781 _Michel Marcus_, Sep 03 2018, following a suggestion from _Felix Fröhlich_
%E A318781 a(33)-a(42) from _Giovanni Resta_, Sep 03 2018