

A188439


Irregular triangle of odd primitive abundant numbers (A006038) in which row n has numbers with n distinct prime factors.


7



945, 1575, 2205, 7425, 78975, 131625, 342225, 570375, 3465, 4095, 5355, 5775, 5985, 6435, 6825, 7245, 8085, 8415, 8925, 9135, 9555, 9765, 11655, 12705, 12915, 13545, 14805, 16695, 18585, 19215, 21105, 22365, 22995, 24885, 26145, 28035, 28215, 29835
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OFFSET

3,1


COMMENTS

The initial row has 8 terms. Row n begins with A188342(n). Dickson proves that each row has a finite number of terms. He lists the first two rows in factored form in his paper. However, as Ferrier and Herzog report, Dickson's tables have many errors. There are 576 odd primitive abundant numbers having 4 distinct prime factors, the last of which is 3^10 5^5 17^4 251^2 = 970969744245403125. The next row, for 5 distinct prime factors, has over 100000 terms.
If the prime factors are counted with multiplicity, then the table starts with row 5, having 121 terms: (945, 1575, 2205, 3465, 4095, ..., 430815, 437745, 442365). Row 6 would start (7425, 28215, 29835, 33345, 34155, ...), and row 7, (81081, 121095, 164835, 182655, 189189, ...).  M. F. Hasler, Jul 27 2016


LINKS

T. D. Noe, Rows n = 3..4, flattened
L. E. Dickson, Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors, American Journal of Mathematics 35 (1913), pp. 413422.
A. Ferrier, Table errata 176, MTAC 4 (1950), 222.
Fritz Herzog, Table Errata 571, Math. Comp. 34 (1980), 652.
T. D. Noe, 576 odd primitive abundant numbers, factored


EXAMPLE

From M. F. Hasler, Jul 27 2016: (Start)
Row 3: 945, 1575, 2205, 7425, 78975, 131625, 342225, 570375;
Row 4: 3465, 4095, 5355, ...(571 more)..., 249450402403828125, 970969744245403125;
Row 5: 15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495, 33915, 35805, ...
Row 6: 692835, 838695, 937365, 1057485, 1130415, 1181895, 1225785, 1263405, ...
Row 7: 22309287, 28129101, 30069039, 34051017, 35888853, 36399363, ...
The first column is A188342 = (945, 3465, 15015, 692835, 22309287, ...) (End)


CROSSREFS

Sequence in context: A006038 A287646 A316116 * A275472 A275066 A127667
Adjacent sequences: A188436 A188437 A188438 * A188440 A188441 A188442


KEYWORD

nonn,tabf


AUTHOR

T. D. Noe, Mar 31 2011


STATUS

approved



