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Atlas › Integer Profiles › Node 72,020,096

72,020,096

27 × 83 × 6779
Abundant Even Composite

72,020,096 factors as 2^7 × 83 × 6779. Its 32 positive divisors give a proper-divisor sum of 73,207,504, so this integer is abundant. The Collatz stopping time is 91 steps.

Prime Factor Structure

Factorization String 2^7 × 83 × 6779
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 145,227,600
Proper Divisor Sum 73,207,504
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #72020087 ← → #72020101

Radix Representation

Decimal 72020096
Binary 100010010101111000010000000 (27 bits)
Octal 0o422570200
Hexadecimal 0x44AF080

Divisor Catalog (32)

1 2 4 8 16 32 64 83 128 166 332 664 1,328 2,656 5,312 6,779 10,624 13,558 27,116 54,232 108,464 216,928 433,856 562,657 867,712 1,125,314 2,250,628 4,501,256 9,002,512 18,005,024 36,010,048 72,020,096

Collatz Trajectory (91 steps to reach 1)

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

72,020,096 36,010,048 18,005,024 9,002,512 4,501,256 2,250,628 1,125,314 562,657 1,687,972 843,986 421,993 1,265,980 632,990 316,495 949,486 474,743 1,424,230 712,115 2,136,346 1,068,173 3,204,520 1,602,260 801,130 400,565 1,201,696 600,848 300,424 150,212 75,106 37,553 112,660 56,330 28,165 84,496 42,248 21,124 10,562 5,281 15,844 7,922 3,961 11,884 5,942 2,971 8,914 4,457 13,372 6,686 3,343 10,030 5,015 15,046 7,523 22,570 11,285 33,856 16,928 8,464 4,232 2,116

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