A111948 -id:A111948 - cp's OEIS frontend

A111947 Admirable Harshad numbers.

12, 20, 24, 30, 40, 42, 54, 70, 84, 102, 114, 120, 140, 222, 224, 234, 270, 308, 364, 402, 476, 644, 1002, 1148, 1204, 1638, 1652, 2022, 2202, 2212, 3164, 3250, 3472, 4172, 6200, 7588, 8204, 8432, 8596, 9424, 10002, 10014, 10724, 10792, 11202, 11228

Offset: 1

Jason Earls, Aug 22 2005

			a(3)=24 because 1+2+3+4+8+12-6 = 24 and 24/6 = 4.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A005349 and A111592.

Cf. A111948.

harsQ[n_] := Divisible[n, Plus @@  IntegerDigits[n]]; admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2]; Select[Range[12000], harsQ[#] && admQ[#] &] (* Amiram Eldar, Oct 27 2019 *)

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

Original entry on oeis.org

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

Jason Earls, Aug 26 2005

			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.

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

Cf. A111592, A005349, A111947, A111948.

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 *)

cp's OEIS Frontend

A111947 Admirable Harshad numbers.

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