λ
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Atlas › Integer Profiles › Node 32,970,314

32,970,314

2 × 13 × 41 × 157 × 197
Deficient Even Composite

32,970,314 factors as 2 × 13 × 41 × 157 × 197. Its 32 positive divisors give a proper-divisor sum of 22,214,662, so this integer is deficient. The Collatz stopping time is 325 steps.

Prime Factor Structure

Factorization String 2 × 13 × 41 × 157 × 197
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 55,184,976
Proper Divisor Sum 22,214,662
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #32970313 ← → #32970319

Radix Representation

Decimal 32970314
Binary 1111101110001011001001010 (25 bits)
Octal 0o175613112
Hexadecimal 0x1F7164A

Divisor Catalog (32)

1 2 13 26 41 82 157 197 314 394 533 1,066 2,041 2,561 4,082 5,122 6,437 8,077 12,874 16,154 30,929 61,858 83,681 105,001 167,362 210,002 402,077 804,154 1,268,089 2,536,178 16,485,157 32,970,314

Collatz Trajectory (325 steps to reach 1)

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

32,970,314 16,485,157 49,455,472 24,727,736 12,363,868 6,181,934 3,090,967 9,272,902 4,636,451 13,909,354 6,954,677 20,864,032 10,432,016 5,216,008 2,608,004 1,304,002 652,001 1,956,004 978,002 489,001 1,467,004 733,502 366,751 1,100,254 550,127 1,650,382 825,191 2,475,574 1,237,787 3,713,362 1,856,681 5,570,044 2,785,022 1,392,511 4,177,534 2,088,767 6,266,302 3,133,151 9,399,454 4,699,727 14,099,182 7,049,591 21,148,774 10,574,387 31,723,162 15,861,581 47,584,744 23,792,372 11,896,186 5,948,093 17,844,280 8,922,140 4,461,070 2,230,535 6,691,606 3,345,803 10,037,410 5,018,705 15,056,116 7,528,058

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