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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
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.
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: A333950 A357697 A248694 * A203087 A278559 A263525
KEYWORD
base,nonn
AUTHOR
Robert G. Wilson v, Sep 16 2002
EXTENSIONS
Edited by M. F. Hasler, Dec 30 2016
STATUS
approved