A381381 a(n) is the smallest positive integer m such that for all integers k >= m distinct positive integers d_1, .., d_r exist with d_1 + .. + d_r = k, 1/d_1 + .. + 1/d_r = 1 and none of the d_i divisible by n.

155, 126, 183, 97, 101, 91, 108, 92, 98, 78, 81, 108, 78, 78, 91, 78, 106, 81, 92, 78, 80, 78, 78, 78, 81, 78, 108, 78, 78, 92, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78

Offset

4,1

Comments

a(n) = 78 for all n > 33. For n < 4 such an a(n) does not exist. - Wouter van Doorn, Aug 13 2025

Links

Table of n, a(n) for n=4..66.

Wouter van Doorn, Partitions with prescribed sum of reciprocals: computational results, arXiv:2502.01409 [math.NT], 2025. See Theorem 1 p. 3.

Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Sequence in context: A377736 A368138 A248657 * A159258 A214472 A259379

Adjacent sequences: A381378 A381379 A381380 * A381382 A381383 A381384

Keyword

nonn,easy

Author

Michel Marcus, Feb 22 2025

Extensions

Name edited, offset corrected, and more terms from Wouter van Doorn, Aug 13 2025

Status

approved