A075460 Odd primitive numbers such that n! divided by product of factorials of all proper divisors of n is not an integer.

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.

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 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

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