cp's OEIS Frontend

A275121 a(n) is the smallest multiple of n that is a practical number.

%I A275121 #26 Jul 27 2019 10:30:19
%S A275121 1,2,6,4,20,6,28,8,18,20,66,12,78,28,30,16,204,18,228,20,42,66,276,24,
%T A275121 100,78,54,28,348,30,496,32,66,204,140,36,666,228,78,40,820,42,860,88,
%U A275121 90,276,1128,48,196,100,204,104,1272,54,220,56,228,348,1416,60
%N A275121 a(n) is the smallest multiple of n that is a practical number.
%C A275121 A rational in (0,1) as a fraction in lowest terms with denominator n, if expressed with denominator a(n) will have a practical-number denominator and can be written as an Egyptian fraction.
%C A275121 Note that a(n) exists for each n; a trivial upper bound is n * gpf(n)# = n * A034386(A006530(n)). - _Charles R Greathouse IV_, Jul 25 2016
%H A275121 Amiram Eldar, <a href="/A275121/b275121.txt">Table of n, a(n) for n = 1..10000</a>
%F A275121 a(n) = n * A210445(n).
%e A275121 For example a(5)=20, indicating that a fraction with denominator 5 can be rewritten as a fraction with denominator 20, which is a practical number. Thus a fraction such as 4/5 can be written as 16/20. The new numerator 16 can be written as the sum of distinct divisors of 20 (16=10+5+1) because 20 is a practical number. The fractions 10/20, 5/20, and 1/20 are each a reciprocal: 1/2, 1/4, and 1/20. Thus 4/5 can be written as the sum of distinct reciprocals (Egyptian fraction expansion) as 4/5 = 1/2 + 1/4 + 1/20.
%o A275121 (PARI) /* First declare the function is_a005153(n) as in A005153 */
%o A275121 a(n) = my(k=1); while(!is_a005153(k*n), k++); k*n \\ _Felix Fröhlich_, Jul 18 2016
%Y A275121 Cf. A005153 (practical numbers), A210445.
%Y A275121 Cf. A006530, A034386.
%K A275121 nonn
%O A275121 1,2
%A A275121 _Lee A. Newberg_, Jul 18 2016
%E A275121 More terms from _Felix Fröhlich_, Jul 18 2016