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A101744 Triangular numbers which are 10-almost primes. 2
32640, 73920, 130816, 165600, 204480, 265356, 294528, 401856, 592416, 839160, 947376, 990528, 1279200, 1445850, 1492128, 1606528, 1842240, 1844160, 2031120, 2049300, 2821500, 2956096, 3571128, 3963520, 4148640, 4250070, 4335040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A101745 contains the indices of this sequence, i.e. T(n) for what values of n are these 10-almost primes.

REFERENCES

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 59, 1987.

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 33-38, 1996.

Dudeney, H. E. Amusements in Mathematics. New York: Dover, pp. 67 and 167, 1970.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Triangular Number.

Eric Weisstein's World of Mathematics, Almost Prime.

FORMULA

a(n) is in the intersection of {A000217} and {A046314}. Integers of the form k*(k+1)/2 which have exactly 10 prime factors.

EXAMPLE

a(1) = 32640 because that is the smallest triangular number which is also a 10-almost prime; specifically T(255) = 255*(255+1)/2 = 32640 = 2^7 * 3 * 5 * 17.

MATHEMATICA

BigOmega[n_Integer]:=Plus@@Last[Transpose[FactorInteger[n]]]; Select[Table[n*(n+1)/2, {n, 2, 5000}], BigOmega[ # ]==10&] (* Ray Chandler, Dec 14 2004 *)

PROG

(PARI) list(lim)=my(v=List(), cur, last=3, n=256, t); while((t=n*(n-1)/2) <= lim, cur=bigomega(n); if(cur+old==11, listput(v, t)); old=cur; n++); Vec(v) \\ Charles R Greathouse IV, Feb 05 2017

CROSSREFS

Cf. A000217, A046314, A068443, A075875, A076578-A076583, A075088, A101745.

Sequence in context: A134949 A134947 A172700 * A013691 A152932 A326382

Adjacent sequences:  A101741 A101742 A101743 * A101745 A101746 A101747

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Dec 14 2004

EXTENSIONS

More terms from Ray Chandler, Dec 14 2004

STATUS

approved

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Last modified January 18 13:38 EST 2022. Contains 350455 sequences. (Running on oeis4.)