A272081 -id:A272081 - cp's OEIS frontend

A272083 Irregular triangle read by rows: strictly decreasing positive integer sequences in lexicographic order with the property that the sum of inverses equals one.

1, 6, 3, 2, 12, 6, 4, 2, 15, 10, 3, 2, 15, 12, 10, 4, 2, 15, 12, 10, 6, 4, 3, 18, 9, 3, 2, 18, 12, 9, 4, 2, 18, 12, 9, 6, 4, 3, 18, 15, 10, 9, 6, 2, 18, 15, 12, 10, 9, 4, 3, 20, 5, 4, 2, 20, 6, 5, 4, 3, 20, 12, 6, 5, 2, 20, 15, 10, 5, 4, 3, 20, 15, 12, 10, 5

Offset: 1

Peter Kagey, Apr 19 2016

			First six rows:
[1]                   because 1/1 = 1.
[6, 3, 2]             because 1/6 + 1/3 + 1/2 = 1.
[12, 6, 4, 2]         because 1/12 + 1/6 + 1/4 + 1/2 = 1.
[15, 10, 3, 2]        because 1/15 + 1/10 + 1/3 + 1/2 = 1.
[15, 12, 10, 4, 2]    because 1/15 + 1/12 + 1/10 + 1/4 + 1/2 = 1.
[15, 12, 10, 6, 4, 3] because 1/15 + 1/12 + 1/10 + 1/6 + 1/4 + 1/3 = 1.

Peter Kagey, Table of n, a(n) for n = 1..1578 (All rows with first term less than or equal to 30.)
Wikipedia, Erdős-Graham problem.

Cf. A073546, A216975, A216993, A272020, A272036, A272081, A272082.

A272034 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is the inverse of an integer.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 36, 38, 64, 128, 256, 512, 1024, 2048, 2056, 2080, 2088, 2090, 4096, 8192, 16384, 16896, 16900, 16902, 16928, 18944, 18952, 18954, 18988, 32768, 65536, 131072, 131328, 131332, 131334, 131360, 133376, 133384, 133386, 133420, 148224, 148256, 148258, 150284

Offset: 1

Michel Marcus, Apr 18 2016

nonn

That is, numbers such that A116416(n) is equal to 1.

The powers of 2 (A000079) form a subsequence.

			For n=36, 38_10=100100_2, and 1/3 + 1/6 = 1/2, the inverse of an integer.

Peter Kagey, Table of n, a(n) for n = 1..354

Cf. A000079, A116416, A116417, A272035, A272036, A272081.

Select[Range[2^18], IntegerQ[1/Total[1/# & /@ Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]]] &] (* Michael De Vlieger, Apr 18 2016 *)

isok(n) = {my(b = Vecrev(binary(n))); numerator(sum(k=1, #b, b[k]/k)) == 1;}

A272082 Irregular triangle read by rows: strictly decreasing positive integer sequences in lexicographic order with the property that the sum of inverses is an integer.

Original entry on oeis.org

1, 6, 3, 2, 6, 3, 2, 1, 12, 6, 4, 2, 12, 6, 4, 2, 1, 15, 10, 3, 2, 15, 10, 3, 2, 1, 15, 12, 10, 4, 2, 15, 12, 10, 4, 2, 1, 15, 12, 10, 6, 4, 3, 15, 12, 10, 6, 4, 3, 1, 18, 9, 3, 2, 18, 9, 3, 2, 1, 18, 12, 9, 4, 2, 18, 12, 9, 4, 2, 1, 18, 12, 9, 6, 4, 3, 18, 12

Offset: 1

Peter Kagey, Apr 19 2016

			First 8 rows:
[1]                because 1/1 is an integer
[6, 3, 2]          because 1/6 + 1/3 + 1/2 = 1.
[6, 3, 2, 1]       because 1/6 + 1/3 + 1/2 + 1/1 = 2.
[12, 6, 4, 2]      because 1/12 + 1/6 + 1/4 + 1/2 = 1.
[12, 6, 4, 2, 1]   because 1/12 + 1/6 + 1/4 + 1/2 + 1/1 = 2.
[15, 10, 3, 2]     because 1/15 + 1/10 + 1/3 + 1/2 = 1.
[15, 10, 3, 2, 1]  because 1/15 + 1/10 + 1/3 + 1/2 + 1/1 = 2.
[15, 12, 10, 4, 2] because 1/15 + 1/12 + 1/10 + 1/4 + 1/2 = 1.

Peter Kagey, Table of n, a(n) for n = 1..4039 (All rows with first term less than or equal to 30.)

Cf. A272020, A272035, A272081, A272083.

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A272083 Irregular triangle read by rows: strictly decreasing positive integer sequences in lexicographic order with the property that the sum of inverses equals one.

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A272034 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is the inverse of an integer.

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A272082 Irregular triangle read by rows: strictly decreasing positive integer sequences in lexicographic order with the property that the sum of inverses is an integer.

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