



1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 277, 302, 328, 356, 386, 417, 449, 482, 517, 553, 592, 632, 673, 715, 759, 804, 852, 902, 953, 1005, 1060, 1120, 1181, 1243, 1306, 1370, 1435, 1501, 1571, 1642
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OFFSET

1,2


COMMENTS

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?


LINKS

Table of n, a(n) for n=1..52.


FORMULA

a(n) = SUM[i=1..n] A038770(i).


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS

Cf. A038770, A034709, A034837, A038769, A038772.
Sequence in context: A161680 A000217 A105340 * A109811 A025747 A025738
Adjacent sequences: A176656 A176657 A176658 * A176660 A176661 A176662


KEYWORD

base,easy,nonn


AUTHOR

Jonathan Vos Post, Apr 23 2010


STATUS

approved



