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

1,1

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: A071395 A362053 A357921 * A245856 A053741 A303609

Adjacent sequences: A335554 A335555 A335556 * A335558 A335559 A335560

Keyword

nonn

Author

David A. Corneth, Jun 14 2020

Status

approved