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A103946 Indices of icosahedral numbers (A006564) which are semiprimes. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A032627 A168006 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

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Last modified January 24 01:20 EST 2021. Contains 340398 sequences. (Running on oeis4.)