cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A366048 For n >= 1, a(n) is the least k >= 1 such that 1/d(k) + … + 1/d(k + n - 1) is an integer, d(i) = A000005(i).

Original entry on oeis.org

1, 2, 1, 25, 54, 7, 53, 65, 6, 22, 51, 49, 343, 209, 416, 624, 17, 18, 338, 410, 1622, 341, 140, 849, 139, 337, 1939, 338, 849, 4365, 2565, 6368, 496, 4366, 132, 8392, 131, 4453, 128, 4173, 127, 487, 123, 4437, 492, 122, 3011, 491, 3724, 4171, 2637, 1231, 1631, 12765, 119
Offset: 1

Views

Author

Ctibor O. Zizka, Sep 27 2023

Keywords

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 ?

Examples

			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.
		

Crossrefs

Programs

  • 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

Extensions

More terms from Michel Marcus, Sep 27 2023
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