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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 October 15 14:07 EDT 2018. Contains 316236 sequences. (Running on oeis4.)