1 + 6 + 14 + 21
A331805 · 42 = 1 + 6 + 14 + 21
OEIS A331805, integers equal to the sum of their nonprime proper divisors. 42 is the first term.
List the numbers that divide 42 evenly, leaving out 42 itself: 1, 2, 3, 6, 7, 14, 21. Cross out the primes 2, 3 and 7. What is left adds up to 1 + 6 + 14 + 21 = 42. Forty-two is the smallest number that does this. The next two known are 1316 and 131,080,256.
What it supports
The first term of OEIS A331805 (G. L. Honaker Jr., 2020), a cousin of the perfect numbers. Its first three terms are an even perfect number times a Carol prime: 6 × 7, 28 × 47 and 8128 × 16127.
What it does not
Not the same object as Primary Pseudoperfect 42 (OEIS A054377): 6 belongs there but not here. Not a claim that every term is a perfect number times a Carol prime: the fourth term is still open, and the smallest candidate is not of that form. Not a filler adjective like abundant or Harshad. Not Adams.
Calculation
Proper divisors of 42: 1, 2, 3, 6, 7, 14, 21. Nonprime ones: 1 + 6 + 14 + 21 = 42.
k equals sigma(k) minus k minus the sum of its distinct prime divisors (OEIS A331805, PARI isok). A brute-force check below 3000 returns only 42 and 1316.
ExactnessExact
Form42
Unitinteger
Strengthhard
When2020
Hung6 October 2026