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A286758
Numbers k such that sigma(k) divides sigma(k!).
1
1, 2, 3, 5, 7, 8, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
OFFSET
1,2
COMMENTS
Conjecture: If p is Fermat prime > 3 from A019434 both values sigma((p-1)!) mod sigma(p-1) and sigma(T(p-1)) mod sigma(p-1) are not 0, where T(n) is the n-th triangular number A000217(n) and n! is the factorial number A000142(n).
LINKS
EXAMPLE
8 is a term because sigma(8!) / sigma(8) = sigma(40320) / sigma(8) = 159120 / 15 = 10608 (integer).
PROG
(Magma) [n: n in [1..100] | (SumOfDivisors(Factorial(n))) mod SumOfDivisors(n) eq 0]
CROSSREFS
Complement of A262812.
All primes (A000040) are terms.
Sequence in context: A194798 A302245 A028728 * A106735 A028743 A082634
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 14 2017
STATUS
approved