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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 (list; graph; refs; listen; history; text; internal format)
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 >= 4, are terms. - Marius A. Burtea, Apr 02 2020

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000

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

Cf. A003132, A005349, A003634.

Sequence in context: A327692 A269234 A160517 * A034087 A117562 A169663

Adjacent sequences:  A072078 A072079 A072080 * A072082 A072083 A072084

KEYWORD

base,nonn,easy

AUTHOR

Labos Elemer, Jun 14 2002

STATUS

approved

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Last modified November 29 05:53 EST 2020. Contains 338756 sequences. (Running on oeis4.)