A240597 Numbers k such that sigma(k) == k (mod 9).

1, 15, 24, 42, 60, 64, 69, 78, 90, 100, 114, 123, 133, 147, 153, 177, 186, 198, 222, 231, 240, 258, 259, 270, 276, 288, 289, 306, 339, 360, 366, 393, 402, 403, 414, 429, 438, 447, 459, 474, 477, 492, 495, 501, 507, 511, 522, 582, 588, 594, 600

Offset: 1

Author

Ivan N. Ianakiev, Sep 13 2014

Keywords

• easy
• nonn

Comments

That is, numbers k that satisfy the following:

A010878(k) = A105852(k) or A010878(k) = A010878(A000203(k)).

A010888(k) = A190998(k) or A010888(k) = A010888(A000203(k)).

Examples

			sigma(15) = 24. 24 == 15 (mod 9), therefore 15 is in the sequence.
		

Links

• Ivan N. Ianakiev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A190998, A010878, A105852, A010888.

Programs

Mathematica

Select[Range[1000],Mod[#,9]==Mod[DivisorSigma[1,#],9]&]

Formula

A010888(a(n)) = A010888(A000203(a(n))).

A010888(a(n)) = A190998(a(n)).