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A118701
Largest prime power that divides the average of twin-prime pairs.
1
4, 3, 4, 9, 5, 7, 5, 9, 17, 27, 23, 25, 9, 64, 11, 19, 16, 27, 47, 13, 29, 7, 27, 11, 29, 19, 25, 103, 107, 11, 81, 137, 23, 13, 49, 17, 43, 25, 59, 13, 128, 41, 71, 43, 31, 11, 17, 121, 19, 31, 67, 81, 139, 283, 41, 149, 16, 313, 23, 25, 37, 169, 347, 29, 64
OFFSET
1,1
LINKS
FORMULA
a(n) = A034699(A014574(n)). - Amiram Eldar, May 25 2024
EXAMPLE
a(10) = 27 since the 10th twin-prime pair is (107, 109) and 108 = 4*27.
MATHEMATICA
Max[Power @@@ FactorInteger[#]] & /@ (Select[Prime[Range[350]], PrimeQ[# + 2] &] + 1) (* Amiram Eldar, May 25 2024 *)
PROG
(PARI) maxpow(n) = {my(f = factor(n)); if(n == 1, 1, vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); }
lista(pmax) = {my(prev = 2); forprime(p = 3, pmax, if(p == prev + 2, print1(maxpow(p - 1), ", ")); prev = p); } \\ Amiram Eldar, May 25 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Greg Huber, Jul 13 2006
EXTENSIONS
More terms from Amiram Eldar, May 25 2024
STATUS
approved