cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A316901 Heinz numbers of integer partitions into relatively prime parts whose reciprocal sum is the reciprocal of an integer.

Original entry on oeis.org

2, 195, 3185, 5467, 6475, 6815, 8455, 10527, 15385, 16401, 17719, 20445, 20535, 21045, 25365, 28897, 40001, 46155, 49841, 50431, 54677, 92449, 101543, 113849, 123469, 137731, 156883, 164255, 171941, 185803, 218855, 228085, 230347, 261457, 267883, 274261
Offset: 1

Views

Author

Gus Wiseman, Jul 16 2018

Keywords

Comments

The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Examples

			5467 is the Heinz number of (20,5,4) and 1/20 + 1/5 + 1/4 = 1/2, so 5467 belongs to the sequence.
The sequence of partitions whose Heinz numbers belong to this sequence begins: (1), (6,3,2), (6,4,4,3), (20,5,4), (12,4,3,3), (15,10,3), (24,8,3), (10,5,5,2)

Links

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A289509, A296150, A316854, A316855, A316856, A316857, A316888-A316904.

Programs

  • Mathematica
    Select[Range[2,100000],And[GCD@@PrimePi/@FactorInteger[#][[All,1]]==1,IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]]&]

A316902 Heinz numbers of aperiodic integer partitions whose reciprocal sum is an integer.

Original entry on oeis.org

2, 18, 72, 147, 162, 195, 250, 288, 294, 390, 500, 588, 648, 780, 1125, 1152, 1176, 1323, 1458, 1560, 1755, 2000, 2250, 2352, 2592, 2646, 3120, 3185, 3510, 4000, 4500, 4608, 4704, 4802, 5292, 6240, 6370, 6475, 6591, 7020, 7581, 8450, 9000, 9408, 10101, 10125
Offset: 1

Views

Author

Gus Wiseman, Jul 16 2018

Keywords

Comments

The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
A partition is aperiodic if its multiplicities are relatively prime.

Examples

			The sequence of partitions whose Heinz numbers belong to this sequence begins: (1), (221), (22111), (442), (22221), (632), (3331), (2211111), (4421), (6321), (33311), (44211), (2222111).

Links

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A296150, A316854, A316855, A316856, A316857, A316888-A316904.

Programs

  • Mathematica
    Select[Range[2,20000],And[GCD@@FactorInteger[#][[All,2]]==1,IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]]&]

A316903 Heinz numbers of aperiodic integer partitions whose reciprocal sum is the reciprocal of an integer.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 65, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 147, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 195, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257
Offset: 1

Views

Author

Gus Wiseman, Jul 16 2018

Keywords

Comments

The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
A partition is aperiodic if its multiplicities are relatively prime.

Links

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A296150, A316854, A316855, A316856, A316857, A316888-A316904.

Programs

  • Mathematica
    Select[Range[2,1000],And[GCD@@FactorInteger[#][[All,2]]==1,IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]]&]
Previous Showing 21-23 of 23 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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