A053020 Numbers which, when expressed as a sum of distinct primes with maximum product, use a non-maximal number of primes.

319, 372, 492, 703, 865, 954, 1584, 1842, 2112, 2118, 2418, 2569, 2575, 2899, 2905, 3078, 3432, 3438, 4212, 4218, 4423, 4429, 5341, 5815, 5821, 6066, 6072, 6323, 6329, 6592, 7132, 7967, 7973, 8254, 8260, 8266, 9502, 9508, 9514, 9839, 9845, 10176, 10182, 11225, 11231

Offset: 1

Author

Adam Atkinson, Feb 23 2000

Keywords

• nonn

Examples

			10 is not in the sequence because 5+3+2 has maximum product AND uses the maximum number of primes (3). (10 = 7+3 is worse in both senses). 319 is the first number for which there's a difference.
		

References

• R. K. Guy, Unsolved Problems Number Theory, 2nd edition, Springer, 1994, F19.

Links

• Adam Atkinson, Table of n, a(n) for n = 1..444
• Adam Atkinson, Sequence A053020
• Adam Atkinson, Sequence A053020 [Local copy, in pdf format, with permission]

Programs

Perl

# See Atkinson link

Extensions

More terms from Adam Atkinson, Aug 23 2020