

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 nonabundant number when factored back.


2



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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..43.


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

Cf. A071395.
Sequence in context: A234367 A071395 A357921 * A245856 A053741 A303609
Adjacent sequences: A335554 A335555 A335556 * A335558 A335559 A335560


KEYWORD

nonn


AUTHOR

David A. Corneth, Jun 14 2020


STATUS

approved



