A316430 Heinz numbers of integer partitions whose length is equal to the GCD of all the parts.

1, 2, 9, 21, 39, 57, 87, 91, 111, 125, 129, 159, 183, 203, 213, 237, 247, 267, 301, 303, 321, 325, 339, 377, 393, 417, 427, 453, 489, 519, 543, 551, 553, 559, 575, 579, 597, 669, 687, 689, 707, 717, 753, 789, 791, 813, 817, 843, 845, 879, 923, 925, 933, 951, 973

Offset

1,2

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Links

Table of n, a(n) for n=1..55.

Example

Sequence of integer partitions whose length is equal to their GCD begins: (), (1), (2,2), (4,2), (6,2), (8,2), (10,2), (6,4), (12,2), (3,3,3), (14,2), (16,2), (18,2), (10,4), (20,2), (22,2), (8,6), (24,2), (14,4), (26,2), (28,2), (6,3,3).

Mathematica

Select[Range[200], PrimeOmega[#]==GCD@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]]&]

Crossrefs

Cf. A056239, A067538, A074761, A143773, A289508, A289509, A296150, A316413, A316431, A316432, A316433.

Sequence in context: A298912 A368187 A005476 * A131476 A023549 A192971

Adjacent sequences: A316427 A316428 A316429 * A316431 A316432 A316433

Keyword

nonn

Author

Gus Wiseman, Jul 02 2018

Status

approved