A247104 Squarefree self-numbers.

3, 5, 7, 31, 42, 53, 86, 97, 110, 143, 154, 165, 187, 209, 211, 222, 233, 255, 266, 277, 299, 310, 323, 334, 345, 367, 389, 411, 413, 435, 446, 457, 479, 501, 514, 547, 569, 591, 602, 613, 615, 626, 659, 670, 681, 703, 714, 727, 749, 771, 782, 793, 815, 817

Offset: 1

Author

Reinhard Zumkeller, Nov 18 2014

Keywords

• nonn
• base

Comments

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

intersection of A005117 and A003052.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]
• Eric Weisstein's World of Mathematics, Self Number
• Wikipedia, Self number

Crossrefs

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

Programs

Haskell

a247104 n = a247104_list !! (n-1)
a247104_list = filter ((== 1) . a008966) $ tail a003052_list

Mathematica

nmax = 1000;
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 *)

Formula

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