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.

3, 5, 7, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 77, 78, 79, 82, 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

Offset: 1

Author

Antti Karttunen, May 10 2022

Keywords

• nonn

Comments

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

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Positions of negative terms in A353757.

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

Cf. also A348749, A353684, A353685.

Programs

PARI

A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A353749(n) = (eulerphi(n)*A064989(n));
A353760(n) = { my(s=sigma(n)); (A353749(s)<A353749(n)); };
isA353758(n) = A353760(n);