cp's OEIS Frontend

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.

%I A100263 #23 May 12 2018 02:17:56
%S A100263 9,14,22,38,46,58,62,74,86,94,106,118,134,142,146,158,166,178,194,202,
%T A100263 206,214,218,254,262,274,278,298,302,314,326,334,346,358,382,386,394,
%U A100263 398,422,446,454,458,466,478,482,502,526,538,542,554,562,566,586,614
%N 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.
%C A100263 It appears that, except for the first term a(1)=9, each term of this sequence is twice a prime.
%C A100263 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
%H A100263 Daniel Mondot, <a href="/A100263/b100263.txt">Table of n, a(n) for n = 1..29865</a>
%e A100263 9 is a Harshad number in bases 3, 4 and 7 (not following pattern);
%e A100263 14 is a Harshad number in bases  7,  8 and 13;
%e A100263 22 is a Harshad number in bases 11, 12 and 21;
%e A100263 38 is a Harshad number in bases 19, 20 and 37;
%e A100263 46 is a Harshad number in bases 23, 24 and 45;
%e A100263 58 is a Harshad number in bases 29, 30 and 57;
%e A100263 62 is a Harshad number in bases 31, 32 and 61;
%e A100263 74 is a Harshad number in bases 37, 38 and 73;
%e A100263 86 is a Harshad number in bases 43, 44 and 85;
%e A100263 94 is a Harshad number in bases 47, 48 and 93;
%e A100263 47 = 94/2, 48 = 94/2 + 1, 93 = 94 - 1. - _Daniel Mondot_, Apr 03 2016
%Y A100263 Cf. A080221, A271311, A271313.
%K A100263 nonn,base
%O A100263 1,1
%A A100263 _John W. Layman_, Nov 10 2004