

A055233


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


8




OFFSET

1,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..6.
Erich Friedman, What's Special About This Number?
Robert Munafo, Notable Properties of Specific Numbers
Carlos Rivera, Puzzle


EXAMPLE

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


MAPLE

with(numtheory): P:=proc(q) local a, b, c, d, k, n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; b:=nops(a);
c:=[]; for k from 1 to b do c:=[op(c), a[k, 1]]; od; c:=sort(c);
d:=0; a:=c[1]; while a<=c[b] do d:=d+a; a:=nextprime(a); od;
if n=d then print(n); fi; fi; od; end: P(10^100); # Paolo P. Lava, May 27 2014


CROSSREFS

Cf. A074036, A055514, A169802.
Sequence in context: A229325 A074225 A055514 * A267626 A189947 A197705
Adjacent sequences: A055230 A055231 A055232 * A055234 A055235 A055236


KEYWORD

nice,nonn


AUTHOR

Carlos Rivera, Jun 21 2000


EXTENSIONS

a(5) found by Jud McCranie, Jul 03 2000
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
454539357304421 confirmed to be the 6th term by Donovan Johnson, Aug 23 2010
Example: removed last (see A055514).  Manuel Valdivia, Nov 19 2011


STATUS

approved



