λ
Harmonic Matrix

9,712,561

9712561
Deficient Odd Prime

9,712,561 has digital root 4. The neighboring primes are 9712543 and 9712567; its proper-divisor sum differs from the starting integer by -9,712,560.

Prime Factor Structure

Factorization String 9712561
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 9,712,562
Proper Divisor Sum 1
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #9712543 ← → #9712567

Radix Representation

Decimal 9712561
Binary 100101000011001110110001 (24 bits)
Octal 0o45031661
Hexadecimal 0x9433B1

Divisor Catalog (2)

Collatz Trajectory (101 steps to reach 1)

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

9,712,561 29,137,684 14,568,842 7,284,421 21,853,264 10,926,632 5,463,316 2,731,658 1,365,829 4,097,488 2,048,744 1,024,372 512,186 256,093 768,280 384,140 192,070 96,035 288,106 144,053 432,160 216,080 108,040 54,020 27,010 13,505 40,516 20,258 10,129 30,388 15,194 7,597 22,792 11,396 5,698 2,849 8,548 4,274 2,137 6,412 3,206 1,603 4,810 2,405 7,216 3,608 1,804 902 451 1,354 677 2,032 1,016 508 254 127 382 191 574 287

More profiles

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