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%I #21 Apr 21 2023 06:29:53
%S 8181,400869,1507005,3918213,11151837,22002273,26669007,47319957,
%T 58170393,73843245,75825981,83488077,94338513,108277641,119656197,
%U 126889821,137740257,163057941,184758813,191992437,199226061,202842873,204768225,220926933,228160557,258457473,264328677,277602471,300496797
%N Odd numbers k for which A003958(sigma(k)) = 2*A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.
%C Odd numbers k such that A351442(k) = 2*A003958(k).
%C Any hypothetical odd term of A005820, if such a term exists, should appear in this sequence, in A347391, and in A016754 (odd squares).
%C None of the first 33 terms is a square, and all of them except 75825981 and 204768225 are multiples of 81. Note that 81 is one of the terms of A008848 (and of A231484), squares whose sum of divisors is also square (with A000203(81) = 121).
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o (PARI)
%o A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
%o isA351448(n) = (n%2 && (A003958(sigma(n)) == 2*A003958(n)));
%Y Odd terms in A351447.
%Y Cf. A000203, A003958, A005820, A008848, A016754, A231484, A339905, A347391, A351442.
%K nonn
%O 1,1
%A _Antti Karttunen_, Feb 12 2022
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