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A379234
Numbers k for which k XOR 2*k = sigma(k), where sigma is the sum of divisors function.
2
312, 428, 672, 760, 5009850
OFFSET
1,1
COMMENTS
Equally, numbers k such that 2*k XOR sigma(k) = k, i.e., k XOR sigma(k) = 2*k.
If it exists, a(6) > 2^33.
FORMULA
{k such that A000203(k) = A048724(k)}.
EXAMPLE
672 has binary expansion 1010100000_2, and 672 XOR 2*672 has binary expansion 11111100000_2 = 2016 (= 63*32) = sigma(672), so 672 is included in this sequence. Notably, as 672 is also a Fibbinary number (in A003714, no adjacent 1-bits), it follows that 672 XOR 2*672 = 3*672, and thus 672 is also a 3-perfect number, A005820.
PROG
(PARI) is_A379234(n) = (bitxor(2*n, n)==sigma(n));
CROSSREFS
Fixed points of A318467.
Subsequence of A379236.
Sequence in context: A308002 A112542 A238099 * A259720 A011774 A011251
KEYWORD
nonn,hard,more
AUTHOR
Antti Karttunen, Jan 04 2025
STATUS
approved