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Numbers which, when expressed as a sum of distinct primes with maximum product, use a non-maximal number of primes.
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%I #39 Aug 24 2020 02:07:27

%S 319,372,492,703,865,954,1584,1842,2112,2118,2418,2569,2575,2899,2905,

%T 3078,3432,3438,4212,4218,4423,4429,5341,5815,5821,6066,6072,6323,

%U 6329,6592,7132,7967,7973,8254,8260,8266,9502,9508,9514,9839,9845,10176,10182,11225,11231

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

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

%H Adam Atkinson, <a href="/A053020/b053020.txt">Table of n, a(n) for n = 1..444</a>

%H Adam Atkinson, <a href="http://www.ghira.mistral.co.uk/maths/A053020/">Sequence A053020</a>

%H Adam Atkinson, <a href="/A053020/a053020.pdf">Sequence A053020</a> [Local copy, in pdf format, with permission]

%e 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.

%o (Perl) # See Atkinson link

%K nonn

%O 1,1

%A _Adam Atkinson_, Feb 23 2000

%E More terms from _Adam Atkinson_, Aug 23 2020