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 A055233 Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor. 8

%I

%S 10,39,155,371,2935561623745,454539357304421

%N Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor.

%C Composite n such that n = p_1 + p_2 + ... + p_k where the p_i are consecutive primes, p_1 is the smallest prime factor of n and p_k is the largest.

%H Robert Munafo, <a href="http://www.mrob.com/pub/math/numbers.html">Notable Properties of Specific Numbers</a>

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_098.htm">Puzzle</a>

%e 10 = 2*5 = 2 + 3 + 5; 39 = 3*13 = 3 + 5 + 7 + 11 + 13; 371 = 7*53 = 7 + 11 + 13 + ... + 53.

%p with(numtheory): P:=proc(q) local a,b,c,d,k,n;

%p for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; b:=nops(a);

%p c:=[]; for k from 1 to b do c:=[op(c),a[k,1]]; od; c:=sort(c);

%p d:=0; a:=c[1]; while a<=c[b] do d:=d+a; a:=nextprime(a); od;

%p if n=d then print(n); fi; fi; od; end: P(10^100); # _Paolo P. Lava_, May 27 2014

%Y Cf. A074036, A055514, A169802.

%K nice,nonn

%O 1,1

%A _Carlos Rivera_, Jun 21 2000

%E a(5) found by _Jud McCranie_, Jul 03 2000

%E Concerning a(6): 454539357304421 is the product of two primes, 3536123 * 128541727 and also the sum of these two plus all the primes in between: 3536123 + 3536129 + 3536131 + ... + 128541719 + 128541727. I do not know if there are any terms in A055233 between 2935561623745 and 454539357304421. (I have searched for values of N satisfying N=Pa*Pb=Pa+...+Pb as far as 5.98*10^16, but this is not quite the same as A055233 or A055514.) - _Robert Munafo_, Nov 20 2002

%E 454539357304421 confirmed to be the 6th term by _Donovan Johnson_, Aug 23 2010

%E Example: removed last (see A055514). - _Manuel Valdivia_, Nov 19 2011

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