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inconsummate numbers
Conway called    a inconsummate number if there is not a number    which divided by its sum of digits gives  .

For example, 47 is not inconsummate because  . On the contrary, 62 is inconsummate because it does not exist a number   such that    = 62.

A related family is that of panconsummate numbers, i.e., those numbers which are not inconsummate in any base.

The following table reports the number of inconsummate numbers up to    for  .

 up to # 101 102 103 104 105 106 107 108 109 0 6 111 1437 16430 183089 1905285 18907944 183706706

The first inconsummate numbers are 62, 63, 65, 75, 84, 95, 161, 173, 195, 216, 261, 266, 272, 276, 326, 371, 372 more terms

Below, the spiral pattern of inconsummate numbers up to  . See the page on prime numbers for an explanation and links to similar pictures.

The smallest 3 × 3 magic square whose entries are consecutive inconsummate numbers is

 289956 289947 289953 289949 289952 289955 289951 289957 289948

Inconsummate numbers can also be... (you may click on names or numbers and on + to get more values)