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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
10, 39, 155, 371, 2935561623745, 454539357304421 (list; graph; refs; listen; history; text; internal format)
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 A0055233 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

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Last modified December 3 18:47 EST 2016. Contains 278745 sequences.