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A131492 Numbers n such that the sum of the Carmichael lambda functions of the divisors is a proper divisor of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..36.

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-Fran├žois 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.

Cf. A039716.

Sequence in context: A114825 A224982 A256085 * A276026 A259718 A090945

Adjacent sequences:  A131489 A131490 A131491 * A131493 A131494 A131495

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jul 29 2007

STATUS

approved

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Last modified February 25 12:46 EST 2018. Contains 299654 sequences. (Running on oeis4.)