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 A075460 Odd primitive numbers such that n! divided by product of factorials of all proper divisors of n is not an integer. 2
 1575, 2835, 3465, 4095, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 8085, 9135, 9765, 11655, 12705, 12915, 13545, 14805, 15015, 15435, 16695, 18585, 19215, 19635, 21105, 21945, 22275, 22365, 22995, 23205, 24885, 25245, 25935, 26145, 26565 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If a number is in the sequence, then all of its multiples would also meet the criterion, but are not included. This is meant by the word "primitive" in the definition. LINKS EXAMPLE 1575 = 3^2*5^2*7 is in the sequence, because the product of the factorials of its proper divisors { 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525 } does not divide 1575!. (For example, the former's 2-adic valuation equals 1588 while the latter's 2-adic valuation equals only 1569.) This is the smallest odd number with this property. - M. F. Hasler, Dec 30 2016 MATHEMATICA f[n_] := n!/Apply[Times, Drop[Divisors[n], -1]! ]; a = {}; Do[b = f[n]; If[ !IntegerQ[b], If[ Select[n/a, IntegerQ] == {}, Print[n]; a = Append[a, n]]], {n, 1, 28213, 2}]; a CROSSREFS Cf. A075071. The first primitive n's with this property (most of which are even) are in A075422. Sequence in context: A125014 A333950 A248694 * A203087 A278559 A263525 Adjacent sequences:  A075457 A075458 A075459 * A075461 A075462 A075463 KEYWORD base,nonn AUTHOR Robert G. Wilson v, Sep 16 2002 EXTENSIONS Edited by M. F. Hasler, Dec 30 2016 STATUS approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)