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Search: id:A131492
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| A131492 |
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Numbers n such that the sum of the Carmichael lambda functions of the divisors is a proper divisor of n. |
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1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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The auxiliary sequence defined by b(n)=sum_{d|n} A002322(d) starts 1,2,3,4,5,6,7,6,9,10,11,10,13,14,11,10,17,18,19,16,15,22,23,14,25,26,27,22,29,...
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REFERENCES
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W. D. Banks and F. Luca, On integers with a special divisibility property, Archivum Mathematicum (BRNO) 42 (2006) pp. 31-42.
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FORMULA
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(sum_{d|n} A002322(d)) | n.
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PROGRAM
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(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, ", ") ) ; ) ; }
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CROSSREFS
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Cf. A002322.
Cf. A039716.
Sequence in context: A158527 A108317 A114825 this_sequence A090945 A140798 A010080
Adjacent sequences: A131489 A131490 A131491 this_sequence A131493 A131494 A131495
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 29 2007
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