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Atlas › Integer Profiles › Node 97,239,126

97,239,126

2 × 3 × 31 × 412 × 311
Abundant Even Composite

97,239,126 factors as 2 × 3 × 31 × 41^2 × 311. Its 48 positive divisors give a proper-divisor sum of 109,190,058, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2 × 3 × 31 × 41^2 × 311
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 206,429,184
Proper Divisor Sum 109,190,058
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #97239097 ← → #97239127

Radix Representation

Decimal 97239126
Binary 101110010111100000001010110 (27 bits)
Octal 0o562740126
Hexadecimal 0x5CBC056

Divisor Catalog (48)

1 2 3 6 31 41 62 82 93 123 186 246 311 622 933 1,271 1,681 1,866 2,542 3,362 3,813 5,043 7,626 9,641 10,086 12,751 19,282 25,502 28,923 38,253 52,111 57,846 76,506 104,222 156,333 312,666 395,281 522,791 790,562 1,045,582 1,185,843 1,568,373 2,371,686 3,136,746 16,206,521 32,413,042 48,619,563 97,239,126

Collatz Trajectory (138 steps to reach 1)

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

97,239,126 48,619,563 145,858,690 72,929,345 218,788,036 109,394,018 54,697,009 164,091,028 82,045,514 41,022,757 123,068,272 61,534,136 30,767,068 15,383,534 7,691,767 23,075,302 11,537,651 34,612,954 17,306,477 51,919,432 25,959,716 12,979,858 6,489,929 19,469,788 9,734,894 4,867,447 14,602,342 7,301,171 21,903,514 10,951,757 32,855,272 16,427,636 8,213,818 4,106,909 12,320,728 6,160,364 3,080,182 1,540,091 4,620,274 2,310,137 6,930,412 3,465,206 1,732,603 5,197,810 2,598,905 7,796,716 3,898,358 1,949,179 5,847,538 2,923,769 8,771,308 4,385,654 2,192,827 6,578,482 3,289,241 9,867,724 4,933,862 2,466,931 7,400,794 3,700,397

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