λ
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Atlas › Integer Profiles › Node 32,767,774

32,767,774

2 × 13 × 41 × 59 × 521
Deficient Even Composite

32,767,774 factors as 2 × 13 × 41 × 59 × 521. Its 32 positive divisors give a proper-divisor sum of 22,480,706, so this integer is deficient. The Collatz stopping time is 232 steps.

Prime Factor Structure

Factorization String 2 × 13 × 41 × 59 × 521
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 55,248,480
Proper Divisor Sum 22,480,706
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #32767771 ← → #32767781

Radix Representation

Decimal 32767774
Binary 1111100111111111100011110 (25 bits)
Octal 0o174777436
Hexadecimal 0x1F3FF1E

Divisor Catalog (32)

1 2 13 26 41 59 82 118 521 533 767 1,042 1,066 1,534 2,419 4,838 6,773 13,546 21,361 30,739 31,447 42,722 61,478 62,894 277,693 399,607 555,386 799,214 1,260,299 2,520,598 16,383,887 32,767,774

Collatz Trajectory (232 steps to reach 1)

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

32,767,774 16,383,887 49,151,662 24,575,831 73,727,494 36,863,747 110,591,242 55,295,621 165,886,864 82,943,432 41,471,716 20,735,858 10,367,929 31,103,788 15,551,894 7,775,947 23,327,842 11,663,921 34,991,764 17,495,882 8,747,941 26,243,824 13,121,912 6,560,956 3,280,478 1,640,239 4,920,718 2,460,359 7,381,078 3,690,539 11,071,618 5,535,809 16,607,428 8,303,714 4,151,857 12,455,572 6,227,786 3,113,893 9,341,680 4,670,840 2,335,420 1,167,710 583,855 1,751,566 875,783 2,627,350 1,313,675 3,941,026 1,970,513 5,911,540 2,955,770 1,477,885 4,433,656 2,216,828 1,108,414 554,207 1,662,622 831,311 2,493,934 1,246,967

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