%I #6 Sep 04 2022 08:26:41

%S 1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231,

%T 253,277,302,328,356,386,417,449,482,517,553,592,632,673,715,759,804,

%U 852,902,953,1005,1060,1120,1181,1243,1306,1370,1435,1501,1571,1642

%N Partial sums of A038770.

%C Partial sums of numbers divisible by at least one of their digits. Identical to triangular numbers A000217 until a(23), then differs, because 23 is the smallest natural number in the complement of A038770 (A038772, i.e., not divisible by at least one of its digits). Hence this partial sum is the triangular numbers minus the partial sums of A038772, properly offset. The subsequence of primes (of course 3 is the largest prime triangular number) in the partial sum begins: 3, 277, 449, 673, 953, 1181, 1571, 1789, 2027. What are the equivalents in bases other than 10?

%F a(n) = Sum_{i=1..n} A038770(i).

%e a(23) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 24 = 277 is prime.

%t Accumulate[Select[Range[110],MemberQ[Divisible[#,Cases[ IntegerDigits[ #], Except[ 0]]], True]&]] (* _Harvey P. Dale_, May 11 2017 *)

%Y Cf. A038770, A034709, A034837, A038769, A038772.

%K base,easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Apr 23 2010