λ
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Atlas › Integer Profiles › Node 82,005,228

82,005,228

22 × 32 × 61 × 107 × 349
Abundant Even Composite

82,005,228 factors as 2^2 × 3^2 × 61 × 107 × 349. Its 72 positive divisors give a proper-divisor sum of 131,262,372, so this integer is abundant. The Collatz stopping time is 130 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 61 × 107 × 349
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 213,267,600
Proper Divisor Sum 131,262,372
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #82005227 ← → #82005269

Radix Representation

Decimal 82005228
Binary 100111000110100110011101100 (27 bits)
Octal 0o470646354
Hexadecimal 0x4E34CEC

Divisor Catalog (60 of 72)

1 2 3 4 6 9 12 18 36 61 107 122 183 214 244 321 349 366 428 549 642 698 732 963 1,047 1,098 1,284 1,396 1,926 2,094 2,196 3,141 3,852 4,188 6,282 6,527 12,564 13,054 19,581 21,289 26,108 37,343 39,162 42,578 58,743 63,867 74,686 78,324 85,156 112,029 117,486 127,734 149,372 191,601 224,058 234,972 255,468 336,087 383,202 448,116

Collatz Trajectory (130 steps to reach 1)

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

82,005,228 41,002,614 20,501,307 61,503,922 30,751,961 92,255,884 46,127,942 23,063,971 69,191,914 34,595,957 103,787,872 51,893,936 25,946,968 12,973,484 6,486,742 3,243,371 9,730,114 4,865,057 14,595,172 7,297,586 3,648,793 10,946,380 5,473,190 2,736,595 8,209,786 4,104,893 12,314,680 6,157,340 3,078,670 1,539,335 4,618,006 2,309,003 6,927,010 3,463,505 10,390,516 5,195,258 2,597,629 7,792,888 3,896,444 1,948,222 974,111 2,922,334 1,461,167 4,383,502 2,191,751 6,575,254 3,287,627 9,862,882 4,931,441 14,794,324 7,397,162 3,698,581 11,095,744 5,547,872 2,773,936 1,386,968 693,484 346,742 173,371 520,114

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