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URL: https://oeis.org/A370745

⇱ A370745 - OEIS

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A370745
Numbers k that have at least one divisor d such that p = k/d-1 is prime and (2*d)|(p-1).
2
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
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
Sequence in context: A074121 A175088 A275671 * A387501 A055670 A141096
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Feb 29 2024
STATUS
approved