λ
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Atlas › Integer Profiles › Node 72,760,648

72,760,648

23 × 37 × 401 × 613
Deficient Even Composite

72,760,648 factors as 2^3 × 37 × 401 × 613. Its 32 positive divisors give a proper-divisor sum of 67,931,312, so this integer is deficient. The Collatz stopping time is 220 steps.

Prime Factor Structure

Factorization String 2^3 × 37 × 401 × 613
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 140,691,960
Proper Divisor Sum 67,931,312
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #72760637 ← → #72760669

Radix Representation

Decimal 72760648
Binary 100010101100011110101001000 (27 bits)
Octal 0o425436510
Hexadecimal 0x4563D48

Divisor Catalog (32)

1 2 4 8 37 74 148 296 401 613 802 1,226 1,604 2,452 3,208 4,904 14,837 22,681 29,674 45,362 59,348 90,724 118,696 181,448 245,813 491,626 983,252 1,966,504 9,095,081 18,190,162 36,380,324 72,760,648

Collatz Trajectory (220 steps to reach 1)

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

72,760,648 36,380,324 18,190,162 9,095,081 27,285,244 13,642,622 6,821,311 20,463,934 10,231,967 30,695,902 15,347,951 46,043,854 23,021,927 69,065,782 34,532,891 103,598,674 51,799,337 155,398,012 77,699,006 38,849,503 116,548,510 58,274,255 174,822,766 87,411,383 262,234,150 131,117,075 393,351,226 196,675,613 590,026,840 295,013,420 147,506,710 73,753,355 221,260,066 110,630,033 331,890,100 165,945,050 82,972,525 248,917,576 124,458,788 62,229,394 31,114,697 93,344,092 46,672,046 23,336,023 70,008,070 35,004,035 105,012,106 52,506,053 157,518,160 78,759,080 39,379,540 19,689,770 9,844,885 29,534,656 14,767,328 7,383,664 3,691,832 1,845,916 922,958 461,479

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