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%I #9 Aug 05 2017 12:52:13
%S 1575,2835,3465,4095,5355,5775,5985,6435,6615,6825,7245,8085,9135,
%T 9765,11655,12705,12915,13545,14805,15015,15435,16695,18585,19215,
%U 19635,21105,21945,22275,22365,22995,23205,24885,25245,25935,26145,26565
%N Odd primitive numbers such that n! divided by product of factorials of all proper divisors of n is not an integer.
%C 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.
%e 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
%t 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
%Y Cf. A075071. The first primitive n's with this property (most of which are even) are in A075422.
%K base,nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 16 2002
%E Edited by _M. F. Hasler_, Dec 30 2016
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