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 (OPAN) 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 were counted with multiplicity, then the table would start 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 [See A287646.]
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. 413-422.
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
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, Mar 31 2011
STATUS
approved