7,752,628

2² × 13 × 29 × 53 × 97

Starting at 7,752,628, the Collatz iteration reaches 1 after 111 steps. The first transition is 3876314; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 13 × 29 × 53 × 97

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 15,558,480

Proper Divisor Sum 7,805,852

Digit Sum / Digital Root 37 (Root: 1)

Adjacent Primes #7752623 ← → #7752643

Radix Representation

Decimal	7752628
Binary	11101100100101110110100 (23 bits)
Octal	0o35445664
Hexadecimal	0x764BB4

Divisor Catalog (48)

1 2 4 13 26 29 52 53 58 97 106 116 194 212 377 388 689 754 1,261 1,378 1,508 1,537 2,522 2,756 2,813 3,074 5,044 5,141 5,626 6,148 10,282 11,252 19,981 20,564 36,569 39,962 66,833 73,138 79,924 133,666 146,276 149,089 267,332 298,178 596,356 1,938,157 3,876,314 7,752,628

Collatz Trajectory (111 steps to reach 1)

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

7,752,628 3,876,314 1,938,157 5,814,472 2,907,236 1,453,618 726,809 2,180,428 1,090,214 545,107 1,635,322 817,661 2,452,984 1,226,492 613,246 306,623 919,870 459,935 1,379,806 689,903 2,069,710 1,034,855 3,104,566 1,552,283 4,656,850 2,328,425 6,985,276 3,492,638 1,746,319 5,238,958 2,619,479 7,858,438 3,929,219 11,787,658 5,893,829 17,681,488 8,840,744 4,420,372 2,210,186 1,105,093 3,315,280 1,657,640 828,820 414,410 207,205 621,616 310,808 155,404 77,702 38,851 116,554 58,277 174,832 87,416 43,708 21,854 10,927 32,782 16,391 49,174

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