A346560 Irregular table read by rows: row n lists the numbers m such that in base n the sum of digits of the divisors of m equals m, where m is written in base 10.

1, 2, 3, 6, 1, 6, 1, 4, 1, 9, 1, 16, 1, 30, 1, 8, 18, 28, 1, 10, 1, 15, 1, 14, 1, 21, 36, 1, 1, 27, 1, 22, 30, 1, 16, 1, 26, 56, 90, 120, 1, 1, 42, 1, 1, 34, 1, 64, 1, 38, 54, 1, 88, 1, 168, 240, 1, 1, 46, 66, 1, 1, 140, 1, 1, 78, 360, 1, 32, 1, 58, 1, 45, 1, 62, 112, 1, 1, 240, 1, 1, 102

Offset

2,2

Comments

See A045885 for the largest number in each base.

See A346561 for bases with no number greater than 1.

Links

Table of n, a(n) for n=2..83.

Scott R. Shannon, Table for n = 2 to n = 250.

Example

For n = 2, 6 is a term as the divisors of 6 written in base 2 are 1, 10, 11, 110, and the sum of the digits of these four divisors is 6.
For n = 10, 15 is a term as the divisors of 15 written in base 10 are 1, 3, 5, 15, and the sum of the digits of these four divisors is 15.
For n = 17, 26 is a term as the divisors of 26 written in base 17 are 1, 2, D, 19 (where 'D' is 13_10) and the sum of the digits of these four divisors is 26.
.
The table begins:
1,2,3,6;
1,6;
1,4;
1,9;
1,16;
1,30;
1,8,18,28;
1,10;
1,15;
1,14;
1,21,36;
1;
1,27;
1,22,30;
1,16;
1,26,56,90,120;
1;
1,42;
1;
1,34;
1,64;
1,38,54;
1,88;
1,168,240;

Crossrefs

Cf. A045885 (largest number in each base), A346561 (bases with no number > 1), A045884, A027750.

Sequence in context: A319191 A124795 A368547 * A084459 A093095 A260611

Adjacent sequences: A346557 A346558 A346559 * A346561 A346562 A346563

Keyword

nonn,base,tabf

Author

Scott R. Shannon, Jul 23 2021

Status

approved