A335557 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.
20, 70, 104, 464, 650, 836, 945, 1575, 1952, 2002, 2205, 3230, 4030, 5830, 7192, 7232, 7425, 7912, 8415, 8925, 9555, 11096, 11132, 11492, 12705, 15028, 17816, 20482, 32128, 32445, 33345, 35650, 40850, 45356, 45885, 46035, 47804, 49875, 51765, 51850, 55796, 57584, 61904
Offset: 1
Keywords
Examples
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.
Crossrefs
Cf. A071395.
Programs
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Mathematica
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 *)