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Numbers k such that the sum of the even aliquot parts of k divides k.
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%I #17 Jul 07 2022 08:11:50

%S 4,6,10,12,14,22,26,34,38,46,56,58,62,74,82,86,94,106,118,122,134,142,

%T 146,158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,

%U 326,334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502

%N Numbers k such that the sum of the even aliquot parts of k divides k.

%H Harry J. Smith, <a href="/A066190/b066190.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 2*A053813(n). - _Amiram Eldar_, Jul 07 2022

%t Do[ d = Drop[ Divisors[ n ], -1 ]; l = Length[ d ]; ev = 0; k = 2; While[ k <= l, If[ EvenQ[ d[ [ k ] ] ], ev = ev + d[ [ k ] ] ]; k++ ]; If[ IntegerQ[ n/ev ], Print[ n ] ], {n, 2, 10^3, 2} ]

%t Select[Range[550],Divisible[#,Total[Select[Most[Divisors[#]],EvenQ]]]&]//Quiet (* _Harvey P. Dale_, Mar 11 2011 *)

%o (PARI) { n=0; for (m=1, 10^9, d=divisors(m); s=0; for (i=2, numdiv(m) - 1, if (d[i]%2 == 0, s += d[i])); if (s > 0 && m%s == 0, write("b066190.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 05 2010

%Y Union of A100484 and A139256.

%Y Cf. A053813.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Dec 15 2001

%E a(56) from _Harry J. Smith_, Feb 05 2010