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- Sparsely_totient_number abstract "In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, n, is sparsely totient if for all m > n, where is Euler's totient function. The first few sparsely totient numbers are:2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630 (sequence A036913 in OEIS).For example, 18 is a sparsely totient number because φ(18) = 6, and any number m > 18 falls into at least one of the following classes:m has a prime factor p ≥ 11, so φ(m) ≥ φ(11) = 10 > φ(18).m is a multiple of 7 and m/7 ≥ 3, so φ(m) ≥ 2φ(7) = 12 > φ(18).m is a multiple of 5 and m/5 ≥ 4, so φ(m) ≥ 2φ(5) = 8 > φ(18).m is a multiple of 3 and m/3 ≥ 7, so φ(m) ≥ 4φ(3) = 8 > φ(18).m is a power of 2 and m ≥ 32, so φ(m) ≥ φ(32) = 16 > φ(18).The concept was introduced by David Masser and Peter Shiu in 1986.".
- Sparsely_totient_number wikiPageExternalLink 1102702441.
- Sparsely_totient_number wikiPageExternalLink 73381.
- Sparsely_totient_number wikiPageID "2011159".
- Sparsely_totient_number wikiPageRevisionID "603648154".
- Sparsely_totient_number hasPhotoCollection Sparsely_totient_number.
- Sparsely_totient_number subject Category:Integer_sequences.
- Sparsely_totient_number type Abstraction100002137.
- Sparsely_totient_number type Arrangement107938773.
- Sparsely_totient_number type Group100031264.
- Sparsely_totient_number type IntegerSequences.
- Sparsely_totient_number type Ordering108456993.
- Sparsely_totient_number type Sequence108459252.
- Sparsely_totient_number type Series108457976.
- Sparsely_totient_number comment "In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, n, is sparsely totient if for all m > n, where is Euler's totient function.".
- Sparsely_totient_number label "Numero scarsamente totiente".
- Sparsely_totient_number label "Sparsely totient number".
- Sparsely_totient_number sameAs Numero_scarsamente_totiente.
- Sparsely_totient_number sameAs m.06dx4n.
- Sparsely_totient_number sameAs Q3879423.
- Sparsely_totient_number sameAs Q3879423.
- Sparsely_totient_number sameAs Sparsely_totient_number.
- Sparsely_totient_number wasDerivedFrom Sparsely_totient_number?oldid=603648154.
- Sparsely_totient_number isPrimaryTopicOf Sparsely_totient_number.