A330872 - OEIS

A330872

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

%I #11 Apr 30 2020 03:25:29

%S 82004,158235,516704,2921535,5801984,10846016,12374144,12603824,

%T 18738224,24252074,32409530,33696975,35356544,36149295,41078114,

%U 42541190,43485584,65090864,88304475,90725775,181480695,183872535,213261795,233762528,242301344,254502495,254630144

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

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

%H Amiram Eldar, <a href="/A330872/b330872.txt">Table of n, a(n) for n = 1..100</a>

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

%t 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

%Y Subsequence of A005101, A071395, A096399 and A283418.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 29 2020