A153134
Numbers k such that 6k - 7 is prime.
Original entry on oeis.org
2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 18, 19, 20, 23, 24, 26, 29, 30, 31, 33, 34, 39, 40, 41, 43, 44, 45, 46, 48, 50, 53, 54, 59, 60, 61, 65, 66, 68, 71, 73, 75, 76, 78, 79, 81, 83, 85, 86, 88, 94, 95, 96, 99, 100, 101, 104, 108, 109, 110, 111, 114, 115, 118, 121, 125, 128
Offset: 1
A153245
Numbers n>1 such that 6*n-7 is not prime.
Original entry on oeis.org
7, 12, 14, 17, 21, 22, 25, 27, 28, 32, 35, 36, 37, 38, 42, 47, 49, 51, 52, 55, 56, 57, 58, 62, 63, 64, 67, 69, 70, 72, 74, 77, 80, 82, 84, 87, 89, 90, 91, 92, 93, 97, 98, 102, 103, 105, 106, 107, 112, 113, 116, 117, 119, 120, 122, 123, 124, 126, 127, 129, 131, 132, 133
Offset: 1
Distribution of the terms in the following triangular array:
*;
*,*;
*,7,*;
*,*,*,*;
*,*,14,*,*;
*,12,*,*,25,*;
*, *,*,*,*, *,*;
*,*,21,*,*,38,*,*;
*,17,*,*,36,*,*,55,*;
*,*, *,*,*, *,*,*, *,*;
*,*,28,*,*,51,*,*,74,*,*;
*,22,*,*,47,*,*,72,*,*,97,*; etc.
where * marks the non-integer values of (2*h*k + k + h + 4)/3 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013
A308643
Odd squarefree composite numbers k, divisible by the sum of their prime factors, sopfr (A001414).
Original entry on oeis.org
105, 231, 627, 805, 897, 1581, 2967, 3055, 4543, 5487, 6461, 6745, 7881, 9717, 10707, 14231, 15015, 16377, 21091, 26331, 29607, 33495, 33901, 33915, 35905, 37411, 38843, 40587, 42211, 45885, 49335, 50505, 51051, 53295, 55581, 60297
Offset: 1
105=3*5*7; sum of prime factors = 15 and 105 = 7*15, so 105 is a term.
-
[k:k in [2*d+1: d in [1..35000]]|IsSquarefree(k) and not IsPrime(k) and k mod &+PrimeDivisors(k) eq 0]; // Marius A. Burtea, Jun 19 2019
-
with(NumberTheory);
N := 500;
for n from 2 to N do
S := PrimeFactors(n);
X := add(S);
if IsSquareFree(n) and not mod(n, 2) = 0 and not isprime(n) and mod(n, X) = 0 then print(n);
end if:
end do:
-
aQ[n_] := Module[{f = FactorInteger[n]}, p=f[[;;,1]]; e=f[[;;,2]]; Length[e] > 1 && Max[e]==1 && Divisible[n, Plus@@(p^e)]]; Select[Range[1, 61000, 2], aQ] (* Amiram Eldar, Jul 04 2019 *)
A153319
Primes p such that 6*p-7 is not prime.
Original entry on oeis.org
7, 17, 37, 47, 67, 89, 97, 103, 107, 113, 127, 131, 137, 151, 157, 167, 179, 181, 191, 197, 223, 227, 233, 257, 277, 281, 283, 293, 307, 311, 317, 337, 347, 359, 367, 373, 383, 389, 397, 419, 421, 439, 443, 457, 461, 463, 467, 479, 487, 499, 509, 523, 541
Offset: 1
-
lst={};Do[p=Prime[n];If[ !PrimeQ[6*p-7],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[100]],!PrimeQ[6#-7]&] (* Harvey P. Dale, Dec 13 2019 *)
Typo in definition fixed by
Zak Seidov, Nov 14 2011
Showing 1-4 of 4 results.
Comments