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 A282572 Integers that are a product of Mersenne numbers A000225, (i.e., product of numbers of the form 2^n - 1). 6
 1, 3, 7, 9, 15, 21, 27, 31, 45, 49, 63, 81, 93, 105, 127, 135, 147, 189, 217, 225, 243, 255, 279, 315, 343, 381, 405, 441, 465, 511, 567, 651, 675, 729, 735, 765, 837, 889, 945, 961, 1023, 1029, 1143, 1215, 1323, 1395, 1519, 1533, 1575, 1701, 1785, 1905, 1953, 2025, 2047, 2187, 2205, 2295, 2401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of terms < 2^k: 1, 2, 3, 5, 8, 11, 15, 22, 30, 41, 55, 74, 98, 128, 167, 217, 279, 355, 451, 572, 718, 901, 1126, 1401, 1731, 2138, 2628, 3222, 3937, 4798, 5833, 7071, 8549, 10312, 12406, 14896, 17845, 21333, 25449, 30310, 36020, 42740, 50612, 59837, 70627, 83233, 97944, 115075, 134995, 158151, 185018, 216167, 252219, 293908, 342057, 397631, 461676, 535438, 620268, 717765, 829684, 958056, 1105140, 1273546, 1466158, 1686304, etc. - Robert G. Wilson v, Feb 23 2017 Odd orders of finite abelian groups that appear as the group of units in a commutative ring (Chebolu and Lockridge, see A296241). - Jonathan Sondow, Dec 15 2017 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 Chebolu, Sunil K., and Keir Lockridge. How many units can a commutative ring have?, arXiv preprint arXiv:1701.02341 (2017). See Th. 8. EXAMPLE 63 = 1*3^3*7, 81 = 1*3^4, 93 = 1*3*31, 105 = 1*7*15, 41013 = 1*3^3*7^2*31; MATHEMATICA lmt = 2500; a = b = Array[2^# - 1 &, Floor@ Log2@ lmt]; k = 2; While[k < Length@ a, e = 1; While[e < Floor@ Log[ a[[k]], lmt], b = Union@ Join[b, Select[ a[[k]]^e*b, # < 1 + lmt &]]; e++]; k++]; b (* Robert G. Wilson v, Feb 23 2017 *) PROG (PARI) forstep(x=1, 1000000, 2, t=x; forstep(n=20, 2, -1, m=2^n-1; while(t%m==0, t=t\m)); if(t==1, print1(x, ", "))) \\ Dmitry Petukhov, Feb 23 2017 CROSSREFS Cf. A000225, A056652, A296241. Note that A191131, A261524, A261871, and A282572 are very similar and easily confused with each other. Sequence in context: A261524 A261871 A191131 * A299642 A128539 A192118 Adjacent sequences:  A282569 A282570 A282571 * A282573 A282574 A282575 KEYWORD nonn AUTHOR Andrew Ivashenko, Feb 18 2017 EXTENSIONS More terms from Michel Marcus, Feb 23 2017 Definition changed by David A. Corneth, Mar 12 2017 STATUS approved

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)