

A109396


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


1



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
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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



