A055009 Smallest composite number x such that sigma(x + prime(n)#) = sigma(x) + prime(n)#, where prime(n)# = A002110(n) and sigma is A000203.

434, 104, 44, 176, 2924, 34256, 83509, 539081, 254963216, 14600541172, 201346999808

Offset: 1

Author

Labos Elemer, May 31 2000

Keywords

• more
• nonn

Comments

a(12) <= 14841476269604. a(13) <= 314064788156864. - Donovan Johnson, Mar 17 2013

Examples

			a(7) = 83509 = 37*37*61, sigma(83509)+510510 = 87234+510510 = sigma(83509+510510) = sigma(594019) = 597744.
		

Crossrefs

The prime solutions for particular sigma(x+primorial) = sigma(x)+primorial equations are in A049481-A049485.

A000203, A002110, A015913-A015917, A049902-A049905, A049481-A049485.

Programs

PARI

a(n)=my(P=prod(i=1,n,prime(i)),x=4); while(isprime(x) || sigma(x+P) != sigma(x)+P, x++); x \\ Charles R Greathouse IV, Feb 14 2013

Extensions

a(9)-a(10) from Donovan Johnson, Oct 15 2008

a(11) from Donovan Johnson, Mar 08 2013