λ
Harmonic Matrix

8,276,992

210 × 59 × 137
Abundant Even Composite

8,276,992 has digital root 7. The neighboring primes are 8276953 and 8276993; its proper-divisor sum differs from the starting integer by 395,176.

Prime Factor Structure

Factorization String 2^10 × 59 × 137
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 44
Divisor Sum (σ) 16,949,160
Proper Divisor Sum 8,672,168
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #8276953 ← → #8276993

Radix Representation

Decimal 8276992
Binary 11111100100110000000000 (23 bits)
Octal 0o37446000
Hexadecimal 0x7E4C00

Divisor Catalog (44)

1 2 4 8 16 32 59 64 118 128 137 236 256 274 472 512 548 944 1,024 1,096 1,888 2,192 3,776 4,384 7,552 8,083 8,768 15,104 16,166 17,536 30,208 32,332 35,072 60,416 64,664 70,144 129,328 140,288 258,656 517,312 1,034,624 2,069,248 4,138,496 8,276,992

Collatz Trajectory (155 steps to reach 1)

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

8,276,992 4,138,496 2,069,248 1,034,624 517,312 258,656 129,328 64,664 32,332 16,166 8,083 24,250 12,125 36,376 18,188 9,094 4,547 13,642 6,821 20,464 10,232 5,116 2,558 1,279 3,838 1,919 5,758 2,879 8,638 4,319 12,958 6,479 19,438 9,719 29,158 14,579 43,738 21,869 65,608 32,804 16,402 8,201 24,604 12,302 6,151 18,454 9,227 27,682 13,841 41,524 20,762 10,381 31,144 15,572 7,786 3,893 11,680 5,840 2,920 1,460

More profiles

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