A302917 Solution to a(1) = 1 and Sum_y Product_i a(y_i) = 0 for each n > 1, where the sum is over all relatively prime or monic partitions of n.

1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, -1, -1, 1, 1, -1, -1, 0, 1, 1, -3, 1, 4, -5, -3, 3, 4, 2, -6, -6, 19, -8, -25, 25, 20, -12, -34, 2, 30, 38, -117, 54, 159, -173, -123, 55, 229, 32, -250, -148, 753, -365, -1022, 840, 1121, -847, -1482, -390, 2099

Offset

1,22

Comments

A relatively prime or monic partition of n is an integer partition of n that is either of length 1 (monic) or whose parts have no common divisor other than 1 (relatively prime).

Links

Table of n, a(n) for n=1..60.

Mathematica

a[n_]:=a[n]=If[n===1, 1, 0]-Sum[Times@@a/@y, {y, Rest[Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&]]}];
Array[a, 20]

Crossrefs

Cf. A000837, A036987, A047966, A063834, A093637, A196545, A220418, A289501, A290261, A300486, A300863-A300866, A301462, A302094, A302915, A302916.

Sequence in context: A319649 A198553 A324288 * A069203 A046070 A068399

Adjacent sequences: A302914 A302915 A302916 * A302918 A302919 A302920

Keyword

sign

Author

Gus Wiseman, Apr 15 2018

Status

approved