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A213071 3*n*(9n + 2)*(18n - 1), where n runs through the odd numbers 1, 3, 5,... 0
561, 13833, 62745, 170625, 360801, 656601, 1081353, 1658385, 2411025, 3362601, 4536441, 5955873, 7644225, 9624825, 11921001, 14556081, 17553393, 20936265, 24728025, 28952001, 33631521, 38789913, 44450505, 50636625, 57371601, 64678761, 72581433, 81102945, 90266625 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Carmichael numbers (561, 62745, 656601, 11921001, 174352641) were obtained for the following values of n: 1, 5, 11, 29, 71.
The sequence can be generalized this way: C = p*n*(3*p*n + 2)*(6*p*n - 1), where p is prime.
Few examples for p from 5 to 23:
For p = 5 the formula becomes 5*n*(15*n + 2)*(30*n - 1) and were obtained the following Carmichael numbers: 2465, 62745, 11119105, 3249390145 (for n = 1, 3, 17, 113);
For p = 7 the formula becomes 7*n*(21*n + 2)*(42*n - 1) and were obtained the following Carmichael numbers: 6601 (for n = 1);
For p = 11 the formula becomes 11*n*(33*n + 2)*(66*n - 1) and were obtained the following Carmichael numbers: 656601 (for n = 3);
For p = 13 the formula becomes 13*n*(39*n + 2)*(78*n - 1) and were obtained the following Carmichael numbers: 41041, 271794601 (for n = 1, 21);
For p = 17 the formula becomes 17*n*(51*n + 2)*(102*n - 1) and were obtained the following Carmichael numbers: 11119105, 2159003281 (for n = 5);
For p = 19 the formula becomes 19*n*(57*n + 2)*(114*n - 1) and were obtained the following Carmichael numbers: 271794601 (for n = 13);
For p = 23 the formula becomes 23*n*(69*n + 2)*(138*n - 1) and were obtained the following Carmichael numbers: 5345340001 (for n = 29).
LINKS
E. W. Weisstein, Carmichael Number
FORMULA
G.f. 3*x*(187+3863*x+3593*x^2+133*x^3) / (x-1)^4 . - R. J. Mathar, Jul 05 2012
a(n) = 3888n^3 - 5508n^2 + 2580n - 399. - Charles R Greathouse IV, Oct 01 2012
PROG
(PARI) a(n)=3888*n^3-5508*n^2+2580*n-399 \\ Charles R Greathouse IV, Oct 01 2012
CROSSREFS
Sequence in context: A063400 A141706 A290485 * A232761 A232755 A264214
KEYWORD
nonn,easy
AUTHOR
Marius Coman, Jun 04 2012
STATUS
approved

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Last modified July 18 09:18 EDT 2024. Contains 374378 sequences. (Running on oeis4.)