Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 May 08 2022 10:33:54
%S 1,114,618,2428,3868,11706,16012,23946,2031108,2938902,3531102,
%T 10475862,98250486,205600756
%N Numbers k for which phi(sigma(k)) + A064989(sigma(k)) is equal to phi(k) + A064989(k).
%C Numbers k such that A353747(k) = A353747(sigma(k)), or equally that A062401(k) + A350073(k) = A000010(k) + A064989(k).
%C When A003961(x) is substituted for k, the condition becomes: numbers x such that phi(A003973(x))+A326042(x) = A003972(x)+x, i.e. A353747(A003973(x)) - x = A003972(x).
%C a(15) > 1442840576, if it exists.
%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o (PARI)
%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o isA353746(n) = { my(s=sigma(n)); ((eulerphi(s)+A064989(s))==(eulerphi(n)+A064989(n))); };
%Y Cf. A000010, A000203, A062401, A064989, A350073, A353747.
%Y Cf. A003961, A003972, A003973, A326042.
%Y Cf. also A348748, A348749, A351440.
%K nonn,more
%O 1,2
%A _Antti Karttunen_, May 06 2022