

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
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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

Table of n, a(n) for n=1..36.


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 2adic valuation equals 1588 while the latter's 2adic 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: A045291 A125014 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



