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URL: https://oeis.org/A349761

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A349761
Numbers k such that sigma(k) = A000203(k) is an abundant number (A005101) and phi(k) = A000010(k) is a deficient number (A005100).
2
6, 10, 11, 15, 17, 20, 22, 23, 24, 30, 34, 40, 46, 47, 51, 53, 59, 60, 68, 69, 80, 83, 85, 92, 94, 96, 102, 106, 107, 118, 120, 131, 136, 137, 138, 141, 149, 160, 166, 167, 170, 173, 177, 179, 188, 191, 204, 214, 227, 233, 235, 236, 239, 240, 249, 251, 255, 257
OFFSET
1,1
COMMENTS
Sándor (2005) proved that this sequence is infinite by showing that it includes all the numbers of the form 3 * 2^k where k == 11 (mod 12). If gcd((k+1)/12, 6) = 1, then this number is also nobly abundant (A349758).
LINKS
EXAMPLE
6 is a term since sigma(6) = 12 is an abundant number, sigma(12) = 28 > 2*12 = 24, and phi(6) = 2 is a deficient number, sigma(2) = 3 < 2*2 = 4.
MATHEMATICA
abQ[n_] := DivisorSigma[1, n] > 2*n; defQ[n_] := DivisorSigma[1, n] < 2*n; q[n_] := abQ[DivisorSigma[1, n]] && defQ[EulerPhi[n]]; Select[Range[250], q]
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 29 2021
STATUS
approved