λ
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Atlas › Integer Profiles › Node 37,937,536

37,937,536

27 × 7 × 13 × 3257
Abundant Even Composite

37,937,536 factors as 2^7 × 7 × 13 × 3257. Its 64 positive divisors give a proper-divisor sum of 55,110,944, so this integer is abundant. The Collatz stopping time is 152 steps.

Prime Factor Structure

Factorization String 2^7 × 7 × 13 × 3257
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 93,048,480
Proper Divisor Sum 55,110,944
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #37937533 ← → #37937563

Radix Representation

Decimal 37937536
Binary 10010000101110000110000000 (26 bits)
Octal 0o220560600
Hexadecimal 0x242E180

Divisor Catalog (60 of 64)

1 2 4 7 8 13 14 16 26 28 32 52 56 64 91 104 112 128 182 208 224 364 416 448 728 832 896 1,456 1,664 2,912 3,257 5,824 6,514 11,648 13,028 22,799 26,056 42,341 45,598 52,112 84,682 91,196 104,224 169,364 182,392 208,448 296,387 338,728 364,784 416,896 592,774 677,456 729,568 1,185,548 1,354,912 1,459,136 2,371,096 2,709,824 2,918,272 4,742,192

Collatz Trajectory (152 steps to reach 1)

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

37,937,536 18,968,768 9,484,384 4,742,192 2,371,096 1,185,548 592,774 296,387 889,162 444,581 1,333,744 666,872 333,436 166,718 83,359 250,078 125,039 375,118 187,559 562,678 281,339 844,018 422,009 1,266,028 633,014 316,507 949,522 474,761 1,424,284 712,142 356,071 1,068,214 534,107 1,602,322 801,161 2,403,484 1,201,742 600,871 1,802,614 901,307 2,703,922 1,351,961 4,055,884 2,027,942 1,013,971 3,041,914 1,520,957 4,562,872 2,281,436 1,140,718 570,359 1,711,078 855,539 2,566,618 1,283,309 3,849,928 1,924,964 962,482 481,241 1,443,724

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