login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055233 Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor. 7
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 * A189947 A197705 A187205

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 26 16:10 EST 2014. Contains 250079 sequences.