A109396 Admirable Harshad numbers such that the subtracted divisor is also a Harshad number.

12, 20, 24, 30, 40, 42, 54, 70, 102, 114, 120, 222, 270, 402, 1002, 2022, 2202, 10002, 10014, 10792, 11202, 12102, 21102, 31002, 32128, 45356, 103002, 110202, 111102, 128768, 740870, 1000002, 1000014, 1001202, 1002102, 1021002, 1111002, 1200102

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Example

12 is in the sequence since it is a Harshad number (1 + 2 = 3 is a divisor of 12), an admirable number: 1 - 2 + 3 + 4 + 6 = 12, and the subtracted divisor, 2, is also a Harshad number.

Mathematica

hQ[n_] := Divisible[n, Plus @@ IntegerDigits@n]; aQ[n_] := hQ[n] && (d = DivisorSigma[1, n] - 2*n) > 0 && EvenQ[d] && d/2 < n && hQ[d/2] && Divisible[n, d/2]; Select[Range[50000], aQ] (* Amiram Eldar, Oct 27 2019 *)

Crossrefs

Cf. A111592, A005349, A111947, A111948.

Sequence in context: A204825 A111592 A111947 * A286004 A055598 A302297

Adjacent sequences: A109393 A109394 A109395 * A109397 A109398 A109399

Keyword

base,nonn

Author

Jason Earls, Aug 26 2005

Status

approved