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

1,1

Comments

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

Links

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

Example

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

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

Crossrefs

Subsequence of A005101, A071395, A096399 and A283418.

Sequence in context: A146025 A361934 A283418 * A253957 A253964 A253760

Adjacent sequences: A330869 A330870 A330871 * A330873 A330874 A330875

Keyword

nonn

Author

Amiram Eldar, Apr 29 2020

Status

approved