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

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, 61, 64, 67, 71, 73, 79, 83, 89, 96, 97, 101, 103, 107, 109, 112, 113, 120, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 192, 193, 197, 199, 211, 223

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n=1..1000

Example

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

Maple

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); # Emeric Deutsch, Feb 26 2005

Mathematica

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} ]

Prog

(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)) ) } \\ Harry J. Smith, Feb 05 2010
(PARI) isok(n) = !(n % sumdiv(n, d, d*(d%2)*(d!=n))); \\ Michel Marcus, Apr 06 2015

Crossrefs

Sequence in context: A100289 A255130 A054021 * A166159 A169693 A180121

Adjacent sequences: A066188 A066189 A066190 * A066192 A066193 A066194

Keyword

nonn,easy

Author

Robert G. Wilson v, Dec 15 2001

Extensions

More terms from Emeric Deutsch, Feb 26 2005

Status

approved