OFFSET
1,1
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David A. Corneth, Jun 14 2020
STATUS
approved