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Squarefree self-numbers.
3

%I #11 Dec 25 2021 18:35:23

%S 3,5,7,31,42,53,86,97,110,143,154,165,187,209,211,222,233,255,266,277,

%T 299,310,323,334,345,367,389,411,413,435,446,457,479,501,514,547,569,

%U 591,602,613,615,626,659,670,681,703,714,727,749,771,782,793,815,817

%N Squarefree self-numbers.

%C Squarefree numbers not expressible as the sum of an integer and its digit sum;

%C intersection of A005117 and A003052.

%H Reinhard Zumkeller, <a href="/A247104/b247104.txt">Table of n, a(n) for n = 1..10000</a>

%H D. R. Kaprekar, <a href="/A003052/a003052_2.pdf">The Mathematics of the New Self Numbers</a> [annotated and scanned]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SelfNumber.html">Self Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Self_number">Self number</a>

%F A008966(a(n)) * (1 - A230093(a(n))) = 1.

%t nmax = 1000;

%t Select[Complement[Range[nmax], Union[Table[n + Total[IntegerDigits[n]], {n, 1, nmax}]]], #>1 && SquareFreeQ[#]&] (* _Jean-François Alcover_, Jan 08 2020, after _T. D. Noe_ in A003052 *)

%o (Haskell)

%o a247104 n = a247104_list !! (n-1)

%o a247104_list = filter ((== 1) . a008966) $ tail a003052_list

%Y Cf. A005117, A003052, A008966, A062028, A006378 (subsequence), A249044.

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Nov 18 2014