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A072081
Numbers divisible by the square of the sum of their digits in base 10.
9
1, 10, 20, 50, 81, 100, 112, 162, 200, 243, 324, 392, 400, 405, 500, 512, 605, 648, 810, 972, 1000, 1053, 1100, 1120, 1134, 1183, 1215, 1296, 1400, 1620, 1701, 1900, 1944, 2000, 2025, 2106, 2156, 2240, 2268, 2300, 2401, 2430, 2511, 2592, 2704, 2800, 2916
OFFSET
1,2
COMMENTS
If k is a term, then 10 * k is a term. There are an infinite number of terms that are not divisible by 10. The numbers m = 24 * 10^(42 * k - 40) +1, k >= 1, are divisible by 7^2 = digsum(m)^2. Also, the numbers s = 491 * 10^(42 * k - 8) + 3, k >= 1, are divisible by 17^2 = digsum(s)^2. - Marius A. Burtea, Mar 19 2020
The numbers 2^A095412(n), n >= 5, are terms. - Marius A. Burtea, Apr 02 2020
LINKS
EXAMPLE
k=9477, sumdigits(9477)=27, q=9477=27*27*13.
MATHEMATICA
sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]^2; If[IntegerQ[n/s], Print[n]], {n, 1, 10000}]
Select[Range[3000], Divisible[#, Total[IntegerDigits[#]]^2]&] (* Harvey P. Dale, May 04 2011 *)
PROG
(PARI) for(n=1, 10^4, s=sumdigits(n); if(!(n%s^2), print1(n, ", "))) \\ Derek Orr, Apr 29 2015
(Magma) [k:k in [1..3000]| k mod &+Intseq(k)^2 eq 0]; // Marius A. Burtea, Mar 19 2020
CROSSREFS
KEYWORD
base,nonn,easy
AUTHOR
Labos Elemer, Jun 14 2002
STATUS
approved