A054982 a(n) = least composite number such that sigma(a(n)+n!) = sigma(a(n))+n! where sigma() = A000203.

434, 104, 80, 182, 427, 1727, 4147, 7163, 42031, 165841, 569257, 2683909, 10040081, 39094849, 155533969, 717519401, 3041377519, 16076525809, 71749935913

Offset: 2

Author

Labos Elemer, May 29 2000

Keywords

• more
• nonn

Comments

a(21) <= 328823468719, a(22) <= 1542201899569, a(23) <= 9325753929619. - Donovan Johnson, Sep 22 2013

Examples

			a(7) = 1727 = 11*157, 4 divisors, sigma(1727)+5040 = 1896+5040 = 6936, sigma(1727+5040) = sigma(6767) = 1+67+101+6767 = 6936.
a(2) = A054799(24) = 434, a(3) = A015914(19) = 104, the first composites in that series.
		

Crossrefs

Cf. A054904, A054905, A054799, A015914, A033560.

Programs

Mathematica

L = {}; Do[i = 1; While[ ! ((Plus @@ Divisors[i + j! ] == j! + Plus @@ Divisors[i]) && ! PrimeQ[i]), i++ ]; L = Append[L, i], {j, 2, 13}]; L (from Vit Planocka)

Extensions

More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 22 2003

a(14)-a(19) from Donovan Johnson, Nov 30 2008

a(20) from Donovan Johnson, Sep 19 2013