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

Author

R. J. Mathar, Jul 29 2007

Keywords

• nonn

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.

Crossrefs

Cf. A002322, A039716.

Programs

Mathematica

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

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,",") ) ; ) ; }

Formula

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