A330872 Numbers k such that k and k+1 are both primitive abundant numbers (A071395).

82004, 158235, 516704, 2921535, 5801984, 10846016, 12374144, 12603824, 18738224, 24252074, 32409530, 33696975, 35356544, 36149295, 41078114, 42541190, 43485584, 65090864, 88304475, 90725775, 181480695, 183872535, 213261795, 233762528, 242301344, 254502495, 254630144

Offset: 1

Author

Amiram Eldar, Apr 29 2020

Keywords

• nonn

Comments

Not to be confused with A283418 in which the primitive abundant numbers can have perfect numbers as divisors (as defined in A091191).

Examples

			82004 is a term since both 82004 and 82005 are abundant, and all of their proper divisors are deficient numbers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Subsequence of A005101, A071395, A096399 and A283418.

Programs

Mathematica

primAbQ[n_] := DivisorSigma[1, n] > 2 n && AllTrue[Most @ Rest @ Divisors[n], DivisorSigma[1, #] < 2*# &]; q1 = False; seq = {}; Do[q2 = primAbQ[n]; If[q1 && q2, AppendTo[seq, n - 1]]; q1 = q2, {n, 2, 6*10^6}]; seq