7,821,513

3² × 7 × 17 × 67 × 109

7,821,513 has digital root 9. The neighboring primes are 7821509 and 7821523; its proper-divisor sum differs from the starting integer by -1,640,466.

Prime Factor Structure

Factorization String 3^2 × 7 × 17 × 67 × 109

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 14,002,560

Proper Divisor Sum 6,181,047

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #7821509 ← → #7821523

Radix Representation

Decimal	7821513
Binary	11101110101100011001001 (23 bits)
Octal	0o35654311
Hexadecimal	0x7758C9

Divisor Catalog (48)

1 3 7 9 17 21 51 63 67 109 119 153 201 327 357 469 603 763 981 1,071 1,139 1,407 1,853 2,289 3,417 4,221 5,559 6,867 7,303 7,973 10,251 12,971 16,677 21,909 23,919 38,913 51,121 65,727 71,757 116,739 124,151 153,363 372,453 460,089 869,057 1,117,359 2,607,171 7,821,513

Collatz Trajectory (142 steps to reach 1)

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

7,821,513 23,464,540 11,732,270 5,866,135 17,598,406 8,799,203 26,397,610 13,198,805 39,596,416 19,798,208 9,899,104 4,949,552 2,474,776 1,237,388 618,694 309,347 928,042 464,021 1,392,064 696,032 348,016 174,008 87,004 43,502 21,751 65,254 32,627 97,882 48,941 146,824 73,412 36,706 18,353 55,060 27,530 13,765 41,296 20,648 10,324 5,162 2,581 7,744 3,872 1,936 968 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233

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