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

1,2

Comments

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

Links

Table of n, a(n) for n=1..73.

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)

Prog

(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);

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.

Sequence in context: A333337 A070089 A371169 * A069167 A331226 A359825

Adjacent sequences: A353756 A353757 A353758 * A353760 A353761 A353762

Keyword

nonn

Author

Antti Karttunen, May 10 2022

Status

approved