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 A066191 Numbers n such that the sum of the odd aliquot parts of n divides n. 1

%I

%S 2,3,4,5,7,8,11,12,13,16,17,19,23,24,29,31,32,37,41,43,47,48,53,56,59,

%T 61,64,67,71,73,79,83,89,96,97,101,103,107,109,112,113,120,127,128,

%U 131,137,139,149,151,157,163,167,173,179,181,191,192,193,197,199,211,223

%N Numbers n such that the sum of the odd aliquot parts of n divides n.

%H Harry J. Smith, <a href="/A066191/b066191.txt">Table of n, a(n) for n=1,...,1000</a>

%e 12 is in the sequence because the odd aliquot parts of 12 are {1,3} and their sum divides 12.

%p with(numtheory):soa:=proc(n) local div,s,j: div:=convert(divisors(n),list): s:=0: for j from 1 to nops(div)-1 do if div[j] mod 2=1 then s:=s+div[j] else s:=s: fi: od: end: p:=proc(n) if type(n/soa(n),integer)=true then n else fi end: seq(p(n),n=1..240); (Deutsch)

%t Do[ d = Drop[ Divisors[ n ], -1 ]; l = Length[ d ]; od = 1; k = 2; While[ k <= l, If[ OddQ[ d[ [ k ] ] ], od = od + d[ [ k ] ] ]; k++ ]; If[ IntegerQ[ n/od ], Print[ n ] ], {n, 2, 200} ]

%o (PARI) { n=0; for (m=2, 10^9, d=divisors(m); s=1; for (i=2, numdiv(m) - 1, if (d[i]%2, s += d[i])); if (s > 0 && m%s == 0, write("b066191.txt", n++, " ", m); if (n==1000, return)) ) } [From _Harry J. Smith_, Feb 05 2010]

%K nonn,easy

%O 1,1

%A _Robert G. Wilson v_, Dec 15 2001

%E More terms from _Emeric Deutsch_, Feb 26 2005

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