A246857 Numbers k such that sigma(k + sigma(k)) = 2*sigma(k).

2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 329, 359, 413, 419, 431, 443, 491, 509, 593, 623, 641, 653, 659, 683, 719, 743, 761, 809, 869, 911, 953, 979, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451

Offset: 1

Author

Jaroslav Krizek, Sep 05 2014

Keywords

• nonn

Comments

Union of A005384 (Sophie Germain primes) and A246858.

First composite number in sequence is 329 (see A246858).

Examples

			Composite number 329 (with sigma(329) = 384) is in sequence because sigma(329+sigma(329)) = sigma(713) = 768 = 2*384.
Prime 359 (with sigma(359) = 360) is in sequence because sigma(359+sigma(359)) = sigma(719) = 720 = 2*360.
		

Crossrefs

Cf. A074400, A246456.

Cf. A005384, A246858.

Programs

Magma

[n:n in[1..10000] | SumOfDivisors(n+SumOfDivisors(n)) eq 2*SumOfDivisors(n)]

Mathematica

Select[Range[1500], DivisorSigma[1, # + DivisorSigma[1, #]] == 2 DivisorSigma[1, #] &] (* Michael De Vlieger, Aug 05 2021 *)

PARI

select(n -> sigma(n+sigma(n))==2*sigma(n),[1..1000]) \\ Edward Jiang, Sep 05 2014