λ
Harmonic Matrix

9,780,827

7 × 1397261
Deficient Odd Composite

9,780,827 has digital root 5. The neighboring primes are 9780821 and 9780829; its proper-divisor sum differs from the starting integer by -8,383,558.

Prime Factor Structure

Factorization String 7 × 1397261
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 11,178,096
Proper Divisor Sum 1,397,269
Digit Sum / Digital Root 41 (Root: 5)
Adjacent Primes #9780821 ← → #9780829

Radix Representation

Decimal 9780827
Binary 100101010011111001011011 (24 bits)
Octal 0o45237133
Hexadecimal 0x953E5B

Divisor Catalog (4)

1 7 1,397,261 9,780,827

Collatz Trajectory (176 steps to reach 1)

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

9,780,827 29,342,482 14,671,241 44,013,724 22,006,862 11,003,431 33,010,294 16,505,147 49,515,442 24,757,721 74,273,164 37,136,582 18,568,291 55,704,874 27,852,437 83,557,312 41,778,656 20,889,328 10,444,664 5,222,332 2,611,166 1,305,583 3,916,750 1,958,375 5,875,126 2,937,563 8,812,690 4,406,345 13,219,036 6,609,518 3,304,759 9,914,278 4,957,139 14,871,418 7,435,709 22,307,128 11,153,564 5,576,782 2,788,391 8,365,174 4,182,587 12,547,762 6,273,881 18,821,644 9,410,822 4,705,411 14,116,234 7,058,117 21,174,352 10,587,176 5,293,588 2,646,794 1,323,397 3,970,192 1,985,096 992,548 496,274 248,137 744,412 372,206

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