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A353758 Numbers k for which A353749(k) > A353749(sigma(k)), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes.

%I A353758 #7 May 11 2022 10:27:02
%S A353758 3,5,7,11,13,14,15,17,19,21,22,23,26,27,29,31,33,34,35,37,38,39,41,42,
%T A353758 43,46,47,51,53,55,57,58,59,61,62,63,65,66,67,69,70,71,73,77,78,79,82,
%U A353758 83,85,86,87,89,91,92,93,94,95,97,99,101,102,103,105,106,107,109,110,111,113,114,115,118,119,122,123,124
%N A353758 Numbers k for which A353749(k) > A353749(sigma(k)), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes.
%C A353758 First odd terms in the intersection of this sequence and A348749 are: 529, 605, 1445, 2825, 6125, 6425, 6875, 7025, ...
%H A353758 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353758 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A353758 (PARI)
%o A353758 A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A353758 A353749(n) = (eulerphi(n)*A064989(n));
%o A353758 A353760(n) = { my(s=sigma(n)); (A353749(s)<A353749(n)); };
%o A353758 isA353758(n) = A353760(n);
%Y A353758 Positions of negative terms in A353757.
%Y A353758 Cf. A353749, A353750, A353759 (complement), A353760 (characteristic function), A353765 (conjectured to be a subsequence).
%Y A353758 Cf. also A348749, A353684, A353685.
%K A353758 nonn
%O A353758 1,1
%A A353758 _Antti Karttunen_, May 10 2022