A353759 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.

1, 2, 4, 6, 8, 9, 10, 12, 16, 18, 20, 24, 25, 28, 30, 32, 36, 40, 44, 45, 48, 49, 50, 52, 54, 56, 60, 64, 68, 72, 74, 75, 76, 80, 81, 84, 88, 90, 96, 98, 100, 104, 108, 112, 116, 117, 120, 121, 126, 128, 132, 136, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 176, 180, 192, 196, 198, 200, 204, 208, 216, 220

Offset: 1

Author

Antti Karttunen, May 10 2022

Keywords

• nonn

Comments

If an odd number is in the intersection of A348749 and A353684, then it is certainly included in this sequence also.

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Positions of nonnegative terms in A353757. Positions of 0's in A353760.

Cf. A353749, A353750, A353758 (complement).

Cf. A007691, A353764 (subsequences).

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)); };
isA353759(n) = !A353760(n);