A329663 - OEIS

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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

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OFFSET

1,1

COMMENTS

a(13) > 1.45*10^11.

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

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

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.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A001065, A030101, A072234.

Sequence in context: A167840 A113917 A259487 * A069793 A230082 A217372

Adjacent sequences: A329660 A329661 A329662 * A329664 A329665 A329666

KEYWORD

nonn,base,more

AUTHOR

Amiram Eldar, Feb 28 2020

EXTENSIONS

a(13) from Giovanni Resta, Feb 29 2020

STATUS

approved