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A075422
Primitive numbers n such that the product of factorials of all proper divisors of n does not divide n!.
3
24, 30, 36, 40, 54, 84, 100, 102, 112, 126, 132, 140, 156, 176, 198, 208, 220, 228, 234, 260, 272, 276, 294, 308, 340, 342, 348, 350, 364, 372, 380, 392, 414, 444, 460, 462, 476, 490, 492, 516, 522, 532, 546, 558, 564, 572, 580, 608, 620, 636, 644, 666, 708
OFFSET
1,1
COMMENTS
If a number is in the sequence, all of its multiples also meet the criterion, but are not included. This is what the word "primitive" refers to.
FORMULA
a(n) appears to be asymptotic to c*n with 12 < c < 15. - Benoit Cloitre, Sep 16 2002
EXAMPLE
The product of the factorials of the proper divisors of 24, 1! * 2! * 3! * 4! * 6! * 8! * 12!, is divisible by 2^26 and therefore does not divide 24! (which is divisible by 2^22 only). 24 is the smallest number with this property. - M. F. Hasler, Dec 31 2016
MATHEMATICA
f[n_] := n!/Apply[Times, Drop[Divisors[n], -1]! ]; a = {}; Do[b = f[n]; If[ !IntegerQ[b], If[ Select[n/a, IntegerQ] == {}, a = Append[a, n]]], {n, 1, 725}]; a
CROSSREFS
Cf. A075071. See A075460 for the odd terms of this sequence.
See A248693 for the list of all (also non-primitive) terms (and PARI code).
Sequence in context: A122181 A167758 A248693 * A230195 A098030 A290451
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by M. F. Hasler, Dec 30 2016
STATUS
approved