A092667 - OEIS

A092667

a(n) = number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k (for any k), with max{x_i}=n.

1, 1, 1, 4, 1, 44, 1, 235, 921, 4038, 1, 66147, 1, 304383, 6581754, 45353329, 1, 1100311690, 1, 44423279911, 1250831952086, 284120133400, 1, 71664788693247, 511162204140999, 55479698795314, 10715917223431762, 505603414069366830, 1, 28696102343693431631, 1, 857699266471525509621, 30399386408588668316839, 63063040603038091480

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..34.

Index entries for sequences related to Egyptian fractions

FORMULA

a(n) = A038034(n) - A038034(n-1).

a(n) = 1 if n is prime.

EXAMPLE

a(4) = 4 since there are four fractions 1=1/2+1/4+1/4, 1=1/4+1/2+1/4, 1=1/4+1/4+1/2 and 1=1/4+1/4+1/4+1/4.

CROSSREFS