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A306650 a(n) = denominator of Sum_{d|n} (d/sigma(d)) where sigma(k) = the sum of the divisors of k (A000203). 1
1, 3, 4, 21, 6, 12, 8, 35, 52, 18, 12, 12, 14, 8, 24, 1085, 18, 156, 20, 126, 32, 36, 24, 20, 186, 14, 520, 56, 30, 72, 32, 9765, 48, 54, 16, 1092, 38, 4, 8, 210, 42, 32, 44, 252, 312, 72, 48, 620, 456, 558, 72, 98, 54, 312, 72, 56, 80, 18, 60, 72, 62, 32, 416 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Sum_{d|n} (d/sigma(d)) >= 1 for all n >= 1.
LINKS
FORMULA
a(p) = p + 1 for primes p.
EXAMPLE
Sum_{d|n} (d/sigma(d)) for n >= 1: 1, 5/3, 7/4, 47/21, 11/6, 35/12, 15/8, 97/35, 127/52, 55/18, 23/12, 47/12, 27/14, ...
For n=4; Sum_{d|4} (d/sigma(d)) = 1/sigma(1) + 2/sigma(2) + 4/sigma(4) = 1/1 + 2/3 + 4/7 = 47/21; a(4) = 21.
PROG
(Magma) [Denominator(&+[d / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = denominator(sumdiv(n, d, d/sigma(d))); \\ Michel Marcus, Mar 03 2019
CROSSREFS
Cf. A000203, A306649 (numerators).
Sequence in context: A009169 A265710 A322673 * A324985 A069934 A206031
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Mar 03 2019
STATUS
approved

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Last modified July 20 06:10 EDT 2024. Contains 374441 sequences. (Running on oeis4.)