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Ratio Atlas
Atlas › Integer Profiles › Node 78,078,752

78,078,752

25 × 19 × 53 × 2423
Abundant Even Composite

78,078,752 factors as 2^5 × 19 × 53 × 2423. Its 48 positive divisors give a proper-divisor sum of 86,850,208, so this integer is abundant. The Collatz stopping time is 148 steps.

Prime Factor Structure

Factorization String 2^5 × 19 × 53 × 2423
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 164,928,960
Proper Divisor Sum 86,850,208
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #78078731 ← → #78078761

Radix Representation

Decimal 78078752
Binary 100101001110110001100100000 (27 bits)
Octal 0o451661440
Hexadecimal 0x4A76320

Divisor Catalog (48)

1 2 4 8 16 19 32 38 53 76 106 152 212 304 424 608 848 1,007 1,696 2,014 2,423 4,028 4,846 8,056 9,692 16,112 19,384 32,224 38,768 46,037 77,536 92,074 128,419 184,148 256,838 368,296 513,676 736,592 1,027,352 1,473,184 2,054,704 2,439,961 4,109,408 4,879,922 9,759,844 19,519,688 39,039,376 78,078,752

Collatz Trajectory (148 steps to reach 1)

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

78,078,752 39,039,376 19,519,688 9,759,844 4,879,922 2,439,961 7,319,884 3,659,942 1,829,971 5,489,914 2,744,957 8,234,872 4,117,436 2,058,718 1,029,359 3,088,078 1,544,039 4,632,118 2,316,059 6,948,178 3,474,089 10,422,268 5,211,134 2,605,567 7,816,702 3,908,351 11,725,054 5,862,527 17,587,582 8,793,791 26,381,374 13,190,687 39,572,062 19,786,031 59,358,094 29,679,047 89,037,142 44,518,571 133,555,714 66,777,857 200,333,572 100,166,786 50,083,393 150,250,180 75,125,090 37,562,545 112,687,636 56,343,818 28,171,909 84,515,728 42,257,864 21,128,932 10,564,466 5,282,233 15,846,700 7,923,350 3,961,675 11,885,026 5,942,513 17,827,540

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