A349762 -id:A349762 - cp's OEIS frontend

A349761 Numbers k such that sigma(k) = A000203(k) is an abundant number (A005101) and phi(k) = A000010(k) is a deficient number (A005100).

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

Amiram Eldar, Nov 29 2021

nonn

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).

			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.

Amiram Eldar, Table of n, a(n) for n = 1..10000
József Sándor, Selected Chapters of Geometry, Analysis and Number Theory, 2005, pp. 132-134.

Cf. A000010, A000203, A005100, A005101, A349758, A349759, A349762.

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]

cp's OEIS Frontend

A349761 Numbers k such that sigma(k) = A000203(k) is an abundant number (A005101) and phi(k) = A000010(k) is a deficient number (A005100).

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