cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A345005 Odd numbers whose arithmetic derivative (A003415) is equal to Dedekind psi (A001615) applied to the same number.

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%I A345005 #14 Jun 07 2021 06:50:32
%S A345005 81,3375,15625,231525,713097,1058841,1500625,4348377,5764801,16891497,
%T A345005 163555875,209548647,239010993,239160735,254205875,267651475,
%U A345005 405189675,451699875,958403475,1050284375,1213014231,1501534375,1695809375,1809323971,1942143291
%N A345005 Odd numbers whose arithmetic derivative (A003415) is equal to Dedekind psi (A001615) applied to the same number.
%C A345005 Conjectured to be also the odd numbers k for which A344998(k) = A344999(k).
%o A345005 (PARI)
%o A345005 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A345005 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A345005 isA345005(n) = ((n%2)&&(A003415(n)==A001615(n)));
%Y A345005 Odd terms in A301939, but see also A345003.
%Y A345005 Cf. A001615, A003415, A344998, A344999.
%K A345005 nonn,more
%O A345005 1,1
%A A345005 _Antti Karttunen_, Jun 05 2021