A359839 Numbers k such that k, k + 1 and k + 2 are 3 consecutive Niven (Harshad) numbers that are also divisible by a square.
2023, 4912, 12103, 17575, 23273, 51424, 52675, 60399, 78650, 80800, 87723, 93624, 100303, 112624, 117962, 121224, 122875, 182182, 193075, 200752, 228175, 235024, 245725, 245726, 249500, 263275, 306963, 320704, 333475, 373490, 403675, 416583, 421072, 444624, 448000
Offset: 1
Examples
2023 = 7 * 17^2 = 289 * (2+0+2+3); 2024 = 506 * 2^2 = 253 * (2+0+2+4) and 2025 = 81 * 5^2 = 225 * (2+0+2+5) hence 2023 is a term.
References
- Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 48, p. 18, Ellipses, Paris, 2008.
- Jean-Marie De Koninck, Those Fascinating Numbers, Entry 110, p. 36, American Mathematical Society, 2009.
Links
- Curtis Cooper and Robert E. Kennedy, On consecutive Niven numbers, Fibonacci Quarterly, Vol. 21, No. 2 (1993), pp. 146-151.
- Giovanni Resta, Harshad numbers.
- Wikipedia, Harshad number.
Crossrefs
Programs
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Mathematica
q[n_] := Divisible[n, Total@IntegerDigits[n]] && ! SquareFreeQ[n]; tri = q /@ Range[3]; seq = {}; Do[tri = Join[Rest[tri], {q[k]}]; If[And @@ tri, AppendTo[seq, k - 2]], {k, 3, 5*10^5}]; seq (* Amiram Eldar, Jan 15 2023 *)
Extensions
More terms from Amiram Eldar, Jan 15 2023
Comments