λ
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Atlas › Integer Profiles › Node 97,277,820

97,277,820

22 × 3 × 5 × 607 × 2671
Abundant Even Composite

97,277,820 factors as 2^2 × 3 × 5 × 607 × 2671. Its 48 positive divisors give a proper-divisor sum of 175,650,948, so this integer is abundant. The Collatz stopping time is 187 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 607 × 2671
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 272,928,768
Proper Divisor Sum 175,650,948
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #97277819 ← → #97277821

Radix Representation

Decimal 97277820
Binary 101110011000101011101111100 (27 bits)
Octal 0o563053574
Hexadecimal 0x5CC577C

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 30 60 607 1,214 1,821 2,428 2,671 3,035 3,642 5,342 6,070 7,284 8,013 9,105 10,684 12,140 13,355 16,026 18,210 26,710 32,052 36,420 40,065 53,420 80,130 160,260 1,621,297 3,242,594 4,863,891 6,485,188 8,106,485 9,727,782 16,212,970 19,455,564 24,319,455 32,425,940 48,638,910 97,277,820

Collatz Trajectory (187 steps to reach 1)

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

97,277,820 48,638,910 24,319,455 72,958,366 36,479,183 109,437,550 54,718,775 164,156,326 82,078,163 246,234,490 123,117,245 369,351,736 184,675,868 92,337,934 46,168,967 138,506,902 69,253,451 207,760,354 103,880,177 311,640,532 155,820,266 77,910,133 233,730,400 116,865,200 58,432,600 29,216,300 14,608,150 7,304,075 21,912,226 10,956,113 32,868,340 16,434,170 8,217,085 24,651,256 12,325,628 6,162,814 3,081,407 9,244,222 4,622,111 13,866,334 6,933,167 20,799,502 10,399,751 31,199,254 15,599,627 46,798,882 23,399,441 70,198,324 35,099,162 17,549,581 52,648,744 26,324,372 13,162,186 6,581,093 19,743,280 9,871,640 4,935,820 2,467,910 1,233,955 3,701,866

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