A100263 Values of n such that A080221(n)=5; i.e., values of n such that n is divisible by the sum of digits of n when expressed in exactly 5 of the bases b=1...n.

9, 14, 22, 38, 46, 58, 62, 74, 86, 94, 106, 118, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 526, 538, 542, 554, 562, 566, 586, 614

Offset: 1

Author

John W. Layman, Nov 10 2004

Keywords

• nonn
• base

Comments

It appears that, except for the first term a(1)=9, each term of this sequence is twice a prime.

Besides base 1, and bases b>=n (bases greater than or equal to the number itself), for which any number can be a Harshad number, these numbers are Harshad numbers in 3 other bases (where b=2..n-1): b1, b2, and b3, where b1 is n/2, b2 is n/2 + 1, b3 is n-1. Except for a(1)=9 that is a Harshad number in bases 3, 4 and 7. - Daniel Mondot, Apr 03 2016

Examples

			9 is a Harshad number in bases 3, 4 and 7 (not following pattern);
14 is a Harshad number in bases  7,  8 and 13;
22 is a Harshad number in bases 11, 12 and 21;
38 is a Harshad number in bases 19, 20 and 37;
46 is a Harshad number in bases 23, 24 and 45;
58 is a Harshad number in bases 29, 30 and 57;
62 is a Harshad number in bases 31, 32 and 61;
74 is a Harshad number in bases 37, 38 and 73;
86 is a Harshad number in bases 43, 44 and 85;
94 is a Harshad number in bases 47, 48 and 93;
47 = 94/2, 48 = 94/2 + 1, 93 = 94 - 1. - _Daniel Mondot_, Apr 03 2016
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..29865

Crossrefs

Cf. A080221, A271311, A271313.