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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

EXAMPLE

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

CROSSREFS

Cf. A080221, A271311, A271313.

Sequence in context: A289548 A001198 A151915 * A155082 A161547 A104812

Adjacent sequences:  A100260 A100261 A100262 * A100264 A100265 A100266

KEYWORD

nonn,base

AUTHOR

John W. Layman, Nov 10 2004

STATUS

approved

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Last modified August 20 08:48 EDT 2019. Contains 326143 sequences. (Running on oeis4.)