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Atlas › Integer Profiles › Node 654,975

654,975

32 × 52 × 41 × 71
Deficient Odd Composite

654,975 factors as 3^2 × 5^2 × 41 × 71. Its 36 positive divisors give a proper-divisor sum of 563,697, so this integer is deficient. The Collatz stopping time is 154 steps.

Prime Factor Structure

Factorization String 3^2 × 5^2 × 41 × 71
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 1,218,672
Proper Divisor Sum 563,697
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #654967 ← → #654991

Radix Representation

Decimal 654975
Binary 10011111111001111111 (20 bits)
Octal 0o2377177
Hexadecimal 0x9FE7F

Divisor Catalog (36)

1 3 5 9 15 25 41 45 71 75 123 205 213 225 355 369 615 639 1,025 1,065 1,775 1,845 2,911 3,075 3,195 5,325 8,733 9,225 14,555 15,975 26,199 43,665 72,775 130,995 218,325 654,975

Collatz Trajectory (154 steps to reach 1)

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

654,975 1,964,926 982,463 2,947,390 1,473,695 4,421,086 2,210,543 6,631,630 3,315,815 9,947,446 4,973,723 14,921,170 7,460,585 22,381,756 11,190,878 5,595,439 16,786,318 8,393,159 25,179,478 12,589,739 37,769,218 18,884,609 56,653,828 28,326,914 14,163,457 42,490,372 21,245,186 10,622,593 31,867,780 15,933,890 7,966,945 23,900,836 11,950,418 5,975,209 17,925,628 8,962,814 4,481,407 13,444,222 6,722,111 20,166,334 10,083,167 30,249,502 15,124,751 45,374,254 22,687,127 68,061,382 34,030,691 102,092,074 51,046,037 153,138,112 76,569,056 38,284,528 19,142,264 9,571,132 4,785,566 2,392,783 7,178,350 3,589,175 10,767,526 5,383,763

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