A370745 Numbers k that have at least one divisor d such that p = k/d-1 is prime and (2*d)|(p-1).

4, 6, 8, 12, 14, 18, 20, 24, 28, 30, 32, 36, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 76, 80, 84, 90, 96, 98, 102, 104, 108, 110, 114, 124, 128, 132, 138, 140, 144, 148, 150, 152, 158, 160, 164, 168, 174, 180, 182, 186, 192, 194, 196, 198, 200, 204, 210, 212, 220

Offset

1,1

Comments

All the terms are even.

Includes all the numbers of the form p+1 where p is an odd prime (A008864 \ {3}).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

D. R. Heath-Brown, Cheryl E. Praeger and Aner Shalev, Permutation groups, simple groups, and sieve methods, Isr. J. Math., Vol. 148 (2005), pp. 347-375; alternative link.

Formula

The number of terms that do not exceed x is N(x) = h * x/log(x) + O(x/log(x)^2), where h = A370746.

Mathematica

q[n_] := AnyTrue[Divisors[n], PrimeQ[n/# - 1] && Divisible[n/# - 2, 2*#] &]; Select[Range[250], q]

Prog

(PARI) is(n) = {my(d = divisors(n)); for(i=1, #d, if(isprime(n/d[i]-1) && !((n/d[i]-2) % (2*d[i])), return(1))); 0; }

Crossrefs

Cf. A008864, A370746.

Sequence in context: A074121 A175088 A275671 * A055670 A141096 A089257

Adjacent sequences: A370742 A370743 A370744 * A370746 A370747 A370748

Keyword

nonn,easy

Author

Amiram Eldar, Feb 29 2024

Status

approved