Arith / CONCEPT
Exponent Normal Form with the Same Number of Distinct Primes
Every positive integer has a companion no larger, with as many distinct primes and non-increasing exponents, whose normalized divisor sum is at least as large.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH2
DOCUMENT LINKS0
A no-larger integer with non-increasing exponents dominates sigma(n)/n
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Coprime prime-exponent normal formstructural-affinity · Closed
- Edge Propagation of Robin's Inequality Along Prime Fibresstructural-affinity · Closed
- Integer Prime Exponent Exchangestructural-affinity · Closed
- Integers Supported on Fibonacci Primesstructural-affinity · Closed
- Mandatory-Core Prime Prefix Normalizationstructural-affinity · Closed
- Prime Padding Ratiostructural-affinity · Closed
- Prime Structure of Actual Price Recordsstructural-affinity · Closed
- Robin's Inequality for Integers with at Most Eight Distinct Primesstructural-affinity · Closed
- Robin's Inequality for the Entire 11-Smooth Familystructural-affinity · Closed
- Robin's Inequality for the Entire 7-Smooth Familystructural-affinity · Closed
- Rough Prime Suffix Maximastructural-affinity · Closed
- Same-integer Robin suffix maximastructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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