A066190 Numbers k such that the sum of the even aliquot parts of k divides k.

4, 6, 10, 12, 14, 22, 26, 34, 38, 46, 56, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502

Offset: 1

Author

Robert G. Wilson v, Dec 15 2001

Keywords

• nonn

Links

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

Crossrefs

Union of A100484 and A139256.

Cf. A053813.

Programs

Mathematica

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} ]
Select[Range[550],Divisible[#,Total[Select[Most[Divisors[#]],EvenQ]]]&]//Quiet  (* Harvey P. Dale, Mar 11 2011 *)

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

Formula

a(n) = 2*A053813(n). - Amiram Eldar, Jul 07 2022

Extensions

a(56) from Harry J. Smith, Feb 05 2010