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

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

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

Links

Table of n, a(n) for n=1..45.

Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.

J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.

Eric Weisstein's World of Mathematics, Semiprime.

Formula

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.

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 an element 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

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

Sequence in context: A168006 A354156 A139960 * A107142 A158018 A226697

Adjacent sequences: A103943 A103944 A103945 * A103947 A103948 A103949

Keyword

nonn

Author

Jonathan Vos Post, Feb 20 2005

Extensions

Edited and extended by Robert G. Wilson v, Feb 21 2005

Status

approved