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%I #8 Aug 01 2020 15:36:28
%S 20,70,104,464,650,836,945,1575,1952,2002,2205,3230,4030,5830,7192,
%T 7232,7425,7912,8415,8925,9555,11096,11132,11492,12705,15028,17816,
%U 20482,32128,32445,33345,35650,40850,45356,45885,46035,47804,49875,51765,51850,55796,57584,61904
%N Primitive abundant numbers version 2 (abundant numbers all of whose proper divisors are deficient numbers) and increasing any prime factor in the prime factorization gives a non-abundant number when factored back.
%e 104 is in the sequence as none of its divisors is abundant and its prime factorization, 2^3 * 13 has the property that when any prime factor is increased to the next prime factor, we get 3^3 * 13 = 351 which isn't abundant (it's then deficient as it's not perfect) or we get 2^3*17 = 136 which is deficient.
%t primabQ[n_] := DivisorSigma[1, n] > 2n && AllTrue[Most @ Divisors[n], DivisorSigma[1, #] < 2# &]; seqQ[n_] := Module[{f = FactorInteger[n]}, p = f[[;; , 1]]; e = f[[;; , 2]]; q = NextPrime[p]; AllTrue[n*(q/p)^e, DivisorSigma[1, #] <= 2# &]]; Select[Range[10^5], primabQ[#] && seqQ[#] &] (* _Amiram Eldar_, Jul 05 2020 *)
%Y Cf. A071395.
%K nonn
%O 1,1
%A _David A. Corneth_, Jun 14 2020
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