OFFSET
1,2
COMMENTS
Conjecture : The sum 1/d(k) + … + 1/d(k + n - 1) = C, C an integer, exists for all k >= 1, n >= 1.
Are there, for some fixed n >= 3, infinitely many k's such that 1/d(k) + … + 1/d(k + n - 1) is an integer ?
EXAMPLE
n = 3: 1/d(k) + 1/d(k + 1) + 1/d(k + 2) = C, C an integer, is valid for the least k = 1, thus a(3) = 1.
n = 4: 1/d(k) + 1/d(k + 1) + 1/d(k + 2) + 1/d(k + 3) = C, C an integer, is valid for the least k = 25, thus a(4) = 25.
PROG
(PARI) a(n) = my(k=1); while (denominator(sum(i=0, n-1, 1/numdiv(k+i))) != 1, k++); k; \\ Michel Marcus, Sep 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Sep 27 2023
EXTENSIONS
More terms from Michel Marcus, Sep 27 2023
STATUS
approved