A131492 Numbers n such that the sum of the Carmichael lambda functions of the divisors is a proper divisor of n.

140, 189, 378, 1375, 2750, 2775, 2997, 4524, 5550, 5661, 5994, 6375, 11253, 11322, 12750, 13416, 13505, 22506, 25925, 27010, 27511, 30613, 32208, 32513, 32760, 45917, 49665, 49959, 51850, 55022, 61061, 61226, 65026, 67488, 91834, 93605

Offset

1,1

Comments

The auxiliary sequence defined by b(n)=sum_{d|n} A002322(d) starts 1,2,3,4,5,6,7,6,9,10,11,10,13,14,11,10,17,18,19,16,...

The auxiliary sequence is A141258. [Reinhard Zumkeller, Feb 17 2012]

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

W. D. Banks and F. Luca, On integers with a special divisibility property, Archivum Mathematicum (BRNO) 42 (2006) pp 31-42.

Formula

n such that (sum_{d|n} A002322(d)) | n.

Mathematica

Select[ Range[100000], Divisible[#, s = Total[ CarmichaelLambda /@ Divisors[#]]] && s < # &] (* Jean-François Alcover, Jun 24 2013 *)

Prog

(PARI) lambda(p, alpha)={ if(p>=3 || alpha<=2, return(p^(alpha-1)*(p-1)), return(2^(alpha-2)) ; ) ; } A002322(n)={ local(pf, rmax, resul) ; if(n==1, return(1) ) ; pf=factor(n) ; rmax=matsize(pf)[1] ; resul= lambda(pf[1, 1], pf[1, 2]) ; for(r=2, rmax, resul=lcm(resul, lambda(pf[r, 1], pf[r, 2])) ; ) ; return(resul) ; } b(n)={ sumdiv(n, d, A002322(d)) ; } { for(n=1, 120000, l=b(n) ; if( l != 1 && l != n && n%l==0, print1(n, ", ") ) ; ) ; }

Crossrefs

Cf. A002322, A039716.

Sequence in context: A224982 A256085 A054573 * A276026 A259718 A090945

Adjacent sequences: A131489 A131490 A131491 * A131493 A131494 A131495

Keyword

nonn

Author

R. J. Mathar, Jul 29 2007

Status

approved