λ
Harmonic Matrix

8,145,223

8145223
Deficient Odd Prime

8,145,223 has digital root 7. The neighboring primes are 8145211 and 8145239; its proper-divisor sum differs from the starting integer by -8,145,222.

Prime Factor Structure

Factorization String 8145223
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 8,145,224
Proper Divisor Sum 1
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #8145211 ← → #8145239

Radix Representation

Decimal 8145223
Binary 11111000100100101000111 (23 bits)
Octal 0o37044507
Hexadecimal 0x7C4947

Divisor Catalog (2)

Collatz Trajectory (199 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

8,145,223 24,435,670 12,217,835 36,653,506 18,326,753 54,980,260 27,490,130 13,745,065 41,235,196 20,617,598 10,308,799 30,926,398 15,463,199 46,389,598 23,194,799 69,584,398 34,792,199 104,376,598 52,188,299 156,564,898 78,282,449 234,847,348 117,423,674 58,711,837 176,135,512 88,067,756 44,033,878 22,016,939 66,050,818 33,025,409 99,076,228 49,538,114 24,769,057 74,307,172 37,153,586 18,576,793 55,730,380 27,865,190 13,932,595 41,797,786 20,898,893 62,696,680 31,348,340 15,674,170 7,837,085 23,511,256 11,755,628 5,877,814 2,938,907 8,816,722 4,408,361 13,225,084 6,612,542 3,306,271 9,918,814 4,959,407 14,878,222 7,439,111 22,317,334 11,158,667

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