A376830 Numbers k such that tau(k + tau(k)) = tau(k) + tau(tau(k)), where tau = A000005.

1, 13, 19, 31, 37, 53, 67, 83, 88, 89, 109, 113, 127, 131, 139, 152, 157, 181, 190, 199, 211, 225, 233, 251, 257, 263, 276, 286, 293, 307, 317, 337, 344, 353, 379, 389, 401, 406, 409, 443, 449, 467, 479, 487, 491, 499, 503, 509, 536, 541, 557, 563, 571, 577, 587, 612, 631, 642, 647, 653, 658, 677

Offset: 1

Author

Robert Israel, Oct 06 2024

Keywords

• nonn

Examples

			a(9) = 88 is a term because tau(88) = 8, tau(8) = 4 and tau(88 + 8) = tau(96) = 12 = 8 + 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A376831, A376843, A376844, A376848, A376849, A376851. Includes A115093.

Programs

Maple

filter:= proc(k) uses numtheory; local s;
 s:= tau(k);
 tau(k+s) = s + tau(s)
end proc:
select(filter, [$1..1000]);

Mathematica

Select[Range[680],DivisorSigma[0,#+DivisorSigma[0,#]]==DivisorSigma[0,#]+DivisorSigma[0,DivisorSigma[0,#]] &] (* Stefano Spezia, Oct 06 2024 *)