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A103946 Indices of icosahedral numbers (A006564) which are semiprimes. 2

%I

%S 37,61,157,193,229,313,373,397,409,433,457,601,613,673,877,997,1009,

%T 1321,1429,1453,1489,1549,1657,1741,1777,1861,2017,2293,2377,2557,

%U 2677,2689,2713,2749,2797,2857,2917,2953,3109,3169,3181,3361,3433,3517,4021

%N Indices of icosahedral numbers (A006564) which are semiprimes.

%D Conway, J. H. and Guy, R. K. The Book of Numbers. New York, Springer-Verlag, p. 50, 1996.

%H Hyun Kwang Kim, <a href="http://dx.doi.org/10.1090/S0002-9939-02-06710-2">On Regular Polytope Numbers</a>, Proc. Amer. Math. Soc., 131 (2003), 65-75.

%H J. V. Post, <a href="http://magicdragon.com/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>

%F n such that A006564(n) is an element of A001358. n such that A102294(n) = 2. n such that A001222(A006564(n)) = 2. n such that Bigomega(n*(5*n2 - 5*n + 2)/2) = 2.

%e 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 an element of A001358, a semiprime because both 7333 and 134413891 are primes.

%t Select[ Prime[ Range[ 557]], PrimeQ[(5#^2 - 5# + 2)/2] &] (* _Robert G. Wilson v_, Feb 21 2005 *)

%o (PARI) isok(n) = bigomega(n*(5*n^2 -5*n + 2)/2) == 2; \\ _Michel Marcus_, Dec 14 2015

%Y Cf. A001222, A001358, A006564, A099186, A102294.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 20 2005

%E Edited and extended by _Robert G. Wilson v_, Feb 21 2005

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Last modified March 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)