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A353807 Numbers k such that A353802(k) / sigma(sigma(k)) is an integer > 1, where A353802(n) = Product_{p^e||n} sigma(sigma(p^e)).

%I A353807 #7 May 08 2022 15:40:25
%S A353807 1819,5088,7215,7276,9487,9523,11895,13303,14235,16371,20179,21079,
%T A353807 21255,24531,24751,24931,25824,29104,30615,32224,33855,36199,37635,
%U A353807 37948,38092,38664,40443,40515,41847,43831,44655,45475,45695,45883,46995,48043,48399,53835,54015,54568,55747,56899,56928,59599,60495,61035
%N A353807 Numbers k such that A353802(k) / sigma(sigma(k)) is an integer > 1, where A353802(n) = Product_{p^e||n} sigma(sigma(p^e)).
%C A353807 Numbers k such that A353805(k) = 1, but A353806(k) > 1.
%H A353807 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A353807 A353802(1819) = 10920 = 2*A051027(1819) = 2*5460, therefore 1819 is included as a term.
%o A353807 (PARI)
%o A353807 A051027(n) = sigma(sigma(n));
%o A353807 A353805(n) = { my(f = factor(n)); (A051027(n) / gcd(A051027(n), prod(k=1, #f~, A051027(f[k, 1]^f[k, 2])))); };
%o A353807 A353806(n) = { my(f = factor(n), u=prod(k=1, #f~, A051027(f[k, 1]^f[k, 2]))); (u / gcd(A051027(n), u)); };
%o A353807 isA353807(n) = ((1==A353805(n)) && (1!=A353806(n)));
%Y A353807 Cf. A000203, A051027, A353802, A353805, A353806.
%Y A353807 Cf. also A336561.
%K A353807 nonn
%O A353807 1,1
%A A353807 _Antti Karttunen_, May 08 2022