A329663 Numbers k such that the binary reversal of k (A030101) is equal to the sum of the proper divisors of k (A001065).

2, 1881, 49905, 54585, 63405, 196785, 853785, 2094897, 3925449, 32480685, 1925817945, 1994453385, 961201916805

Offset: 1

Author

Amiram Eldar, Feb 28 2020

Keywords

• nonn
• base
• more

Comments

a(13) > 1.45*10^11.

a(14) > 5*10^12, if it exists. - Giovanni Resta, Feb 29 2020

Examples

			2 is a term since its binary representation is 10, its binary reversal is 01 = 1 which is equal to the sum of the proper divisors of 2.
1881 is a term since its binary representation is 11101011001, its binary reversal is 10011010111 which is equal to 1239, which is also the sum of the proper divisors of 1881: 1 + 3 + 9 + 11 + 19 + 33 + 57 + 99 + 171 + 209 + 627 = 1239.
		

Crossrefs

Cf. A001065, A030101, A072234.

Programs

Mathematica

Select[Range[10^5], DivisorSigma[1, #] - # == IntegerReverse[#, 2] &]

PARI

isok(k) = sigma(k) - k == fromdigits(Vecrev(binary(k)), 2); \\ Michel Marcus, Feb 29 2020

Extensions

a(13) from Giovanni Resta, Feb 29 2020