A067540 Number of partitions of n in which the sum of reciprocal of parts divides number of parts.

1, 2, 2, 3, 2, 4, 2, 5, 5, 7, 4, 8, 5, 7, 5, 10, 5, 16, 8, 20, 9, 20, 10, 25, 13, 30, 21, 34, 32, 46, 35, 58, 48, 66, 59, 97, 65, 109, 94, 125, 112, 154, 133, 191, 154, 224, 195, 265, 236, 308, 289, 388, 353, 475, 424, 575, 528, 693, 661, 835

Offset: 1

Author

Naohiro Nomoto, Jan 27 2002

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..147 (n = 1..80 from Sean A. Irvine)

Crossrefs

Cf. A000041.

Formula

a(n)=#{n=p_1+p_2+...+p_r : r/sum_{i=1..r} 1/p_i is an integer} where n=p_1+p_2+...+p_r runs over all partitions of n. - Sean A. Irvine, Mar 24 2013

a(n) <= A058360(n) <= A000041(n). - Charles R Greathouse IV, Dec 15 2020

Extensions

More terms from Sean A. Irvine, Mar 24 2013