A137923 -id:A137923 - cp's OEIS frontend

A138566 Numbers n whose digits satisfy the following Diophantine equation: P = (X1* ... *Xr)/(X1+ ... +Xr), where P = prime number, Xi = digits of n.

36, 44, 63, 66, 138, 145, 154, 159, 167, 176, 183, 195, 224, 235, 242, 253, 257, 275, 279, 297, 318, 325, 333, 345, 352, 354, 357, 375, 381, 415, 422, 435, 451, 453, 514, 519, 523, 527, 532, 534, 537, 541, 543, 572, 573, 591, 617, 671, 716, 725, 729, 735

Offset: 1

Ctibor O. Zizka, May 12 2008

			n = 761, we have (7*6*1)/(7+6+1) = 3; a(56)= 761.
n = 792, we have (7*9*2)/(7+9+2) = 7; a(57)= 792.
n = 813, we have (8*1*3)/(8+1+3) = 2; a(58)= 813.

Subsequence of A038367.

Cf. A137923.

Block[{i = k, r = {}}, r = Table[p = IntegerDigits@i; If[PrimeQ[Times @@ p/Total@p], k, Nothing], {k, 735}];r] (* Mikk Heidemaa, May 26 2024 *)

A140281 A Diophantine equation over digits of n. Numbers n such that x_1/r +x_2/r-1 + ... + x_r/1 = k; x_i digits of n; k integer.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 320, 321, 322, 323, 324, 325, 326

Offset: 0

Ctibor O. Zizka, May 23 2008

			n=321 : 3/3 + 2/2 + 1/1 = 3, 321 belongs to the sequence

Cf. A005349, A137923, A138566, A139749, A139750, .

Join[{0},Select[Range[400],IntegerQ[Total[IntegerDigits[#]/Reverse[ Range[ IntegerLength[ #]]]]]&]] (* Harvey P. Dale, May 17 2016 *)

cp's OEIS Frontend

A138566 Numbers n whose digits satisfy the following Diophantine equation: P = (X1* ... *Xr)/(X1+ ... +Xr), where P = prime number, Xi = digits of n.

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