A333967 Subsequence of A071395. The extra constraint is m is not a term if m*q/p is abundant where prime p|m and q is the least prime larger than p.

70, 2002, 3230, 4030, 5830, 8415, 8925, 20482, 32445, 45885, 51765, 83265, 107198, 131054, 133042, 178486, 206770, 253270, 253946, 258970, 270470, 310930, 330310, 334305, 362710, 442365, 474045, 497835, 513890, 544310, 567765, 589095, 592670, 602175, 617265, 631670, 654675

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..1317

Example

70 is in the sequence as it's abundant. Its prime factorization is 2 * 5 * 7. Each of 3 * 5 * 7, 2 * 7 * 7 and 2 * 5 * 11 are deficient and no divisor of 70 is in this sequence.

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), DivisorSigma[1, #] <= 2# &]]; Select[Range[10^5], primabQ[#] && seqQ[#] &] (* Amiram Eldar, Jul 05 2020 *)

Crossrefs

Cf. A071395, A071927, A335557.

Sequence in context: A006296 A047835 A133312 * A093757 A163022 A271031

Adjacent sequences: A333964 A333965 A333966 * A333968 A333969 A333970

Keyword

nonn

Author

David A. Corneth, Jul 05 2020

Status

approved