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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.
5

%I #7 May 11 2022 10:27:02

%S 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 43,46,47,51,53,55,57,58,59,61,62,63,65,66,67,69,70,71,73,77,78,79,82,

%U 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 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 First odd terms in the intersection of this sequence and A348749 are: 529, 605, 1445, 2825, 6125, 6425, 6875, 7025, ...

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</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 A353749(n) = (eulerphi(n)*A064989(n));

%o A353760(n) = { my(s=sigma(n)); (A353749(s)<A353749(n)); };

%o isA353758(n) = A353760(n);

%Y Positions of negative terms in A353757.

%Y Cf. A353749, A353750, A353759 (complement), A353760 (characteristic function), A353765 (conjectured to be a subsequence).

%Y Cf. also A348749, A353684, A353685.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 10 2022