Digit Sum Computation
Calculate the sum of all digits in a number to establish the foundational relationship.
Tools / Mathematical Discovery
resonance
$0.10 per call
Discover the harmonic relationship between numbers and their digit sums. resonance finds common divisors between n and its digit sum—revealing mathematical resonance where numbers align with their own structure.
Capabilities
Common Divisor Analysis
Find all divisors shared between a number and its digit sum.
Resonance Scoring
Calculate a resonance score based on the sum of common divisors.
Niven Number Detection
Identify numbers divisible by their digit sum showing strong resonance.
API Demo
resonance
// Request
{"name": "resonance", "arguments": {"n": 6}}
// Response
{
"n": 6,
"digit_sum": 6,
"common_divisors": [1, 2, 3, 6],
"resonance": 12
}
Note: 6 has perfect resonance—it equals its own digit sum!
Use Cases
Perfect Resonance
Numbers that equal their digit sum (1-9) have maximum resonance for their size.
Niven Numbers
Numbers divisible by their digit sum (like 12, 18, 21) show strong resonance.
Research Applications
Resonance patterns connect to divisibility rules and number theory conjectures.
Discover mathematical harmonics
Explore resonance patterns between numbers and their digit sums. $0.10 per call.
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