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A103946
Indices of icosahedral numbers (A006564) which are semiprimes.
3
37, 61, 157, 193, 229, 313, 373, 397, 409, 433, 457, 601, 613, 673, 877, 997, 1009, 1321, 1429, 1453, 1489, 1549, 1657, 1741, 1777, 1861, 2017, 2293, 2377, 2557, 2677, 2689, 2713, 2749, 2797, 2857, 2917, 2953, 3109, 3169, 3181, 3361, 3433, 3517, 4021
OFFSET
1,1
REFERENCES
J. H. Conway and R. K. Guy, The Book of Numbers, New York, Springer-Verlag, p. 50, 1996.
LINKS
Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.
Eric Weisstein's World of Mathematics, Semiprime.
FORMULA
Numbers k such that A006564(k) is a term of A001358.
Numbers k such that A102294(k) = 2.
Numbers k such that A001222(A006564(k)) = 2.
Numbers k such that Bigomega(k*(5*k^2 - 5*k + 2)/2) = 2.
EXAMPLE
a(69) = 7333 because the 69th icosahedral number to be a semiprime is A006564(7333) = 7333 * (5*73332 - 5*7333 + 2)/2 = 985657062703 = 7333 * 134413891, which is a term of A001358, a semiprime because both 7333 and 134413891 are primes.
MATHEMATICA
Select[ Prime[ Range[ 557]], PrimeQ[(5#^2 - 5# + 2)/2] &] (* Robert G. Wilson v, Feb 21 2005 *)
PROG
(PARI) isok(n) = bigomega(n*(5*n^2 -5*n + 2)/2) == 2; \\ Michel Marcus, Dec 14 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Feb 20 2005
EXTENSIONS
Edited and extended by Robert G. Wilson v, Feb 21 2005
STATUS
approved