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Atlas › Integer Profiles › Node 78,124,256

78,124,256

25 × 7 × 348769
Abundant Even Composite

78,124,256 factors as 2^5 × 7 × 348769. Its 24 positive divisors give a proper-divisor sum of 97,655,824, so this integer is abundant. The Collatz stopping time is 117 steps.

Prime Factor Structure

Factorization String 2^5 × 7 × 348769
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 175,780,080
Proper Divisor Sum 97,655,824
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #78124243 ← → #78124273

Radix Representation

Decimal 78124256
Binary 100101010000001010011100000 (27 bits)
Octal 0o452012340
Hexadecimal 0x4A814E0

Divisor Catalog (24)

1 2 4 7 8 14 16 28 32 56 112 224 348,769 697,538 1,395,076 2,441,383 2,790,152 4,882,766 5,580,304 9,765,532 11,160,608 19,531,064 39,062,128 78,124,256

Collatz Trajectory (117 steps to reach 1)

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

78,124,256 39,062,128 19,531,064 9,765,532 4,882,766 2,441,383 7,324,150 3,662,075 10,986,226 5,493,113 16,479,340 8,239,670 4,119,835 12,359,506 6,179,753 18,539,260 9,269,630 4,634,815 13,904,446 6,952,223 20,856,670 10,428,335 31,285,006 15,642,503 46,927,510 23,463,755 70,391,266 35,195,633 105,586,900 52,793,450 26,396,725 79,190,176 39,595,088 19,797,544 9,898,772 4,949,386 2,474,693 7,424,080 3,712,040 1,856,020 928,010 464,005 1,392,016 696,008 348,004 174,002 87,001 261,004 130,502 65,251 195,754 97,877 293,632 146,816 73,408 36,704 18,352 9,176 4,588 2,294

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