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Atlas › Integer Profiles › Node 3,677,568

3,677,568

27 × 3 × 61 × 157
Abundant Even Composite

3,677,568 factors as 2^7 × 3 × 61 × 157. Its 64 positive divisors give a proper-divisor sum of 6,314,352, so this integer is abundant. The Collatz stopping time is 159 steps.

Prime Factor Structure

Factorization String 2^7 × 3 × 61 × 157
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 9,991,920
Proper Divisor Sum 6,314,352
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #3677567 ← → #3677573

Radix Representation

Decimal 3677568
Binary 1110000001110110000000 (22 bits)
Octal 0o16016600
Hexadecimal 0x381D80

Divisor Catalog (60 of 64)

1 2 3 4 6 8 12 16 24 32 48 61 64 96 122 128 157 183 192 244 314 366 384 471 488 628 732 942 976 1,256 1,464 1,884 1,952 2,512 2,928 3,768 3,904 5,024 5,856 7,536 7,808 9,577 10,048 11,712 15,072 19,154 20,096 23,424 28,731 30,144 38,308 57,462 60,288 76,616 114,924 153,232 229,848 306,464 459,696 612,928

Collatz Trajectory (159 steps to reach 1)

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

3,677,568 1,838,784 919,392 459,696 229,848 114,924 57,462 28,731 86,194 43,097 129,292 64,646 32,323 96,970 48,485 145,456 72,728 36,364 18,182 9,091 27,274 13,637 40,912 20,456 10,228 5,114 2,557 7,672 3,836 1,918 959 2,878 1,439 4,318 2,159 6,478 3,239 9,718 4,859 14,578 7,289 21,868 10,934 5,467 16,402 8,201 24,604 12,302 6,151 18,454 9,227 27,682 13,841 41,524 20,762 10,381 31,144 15,572 7,786 3,893

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