A064481 - OEIS

A064481

Numbers which are divisible by the sum of their base-5 digits.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 24, 25, 26, 27, 28, 30, 32, 36, 40, 42, 45, 48, 50, 51, 52, 54, 56, 60, 63, 64, 65, 66, 72, 75, 76, 78, 80, 85, 88, 90, 91, 96, 99, 100, 102, 104, 105, 112, 117, 120, 125, 126, 128, 130, 132, 135, 136, 138, 140, 144, 145

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Also called 5-Harshad or 5-Niven numbers. - Paolo Xausa, May 03 2026

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Harshad Number.

Wikipedia, Harshad number.

EXAMPLE

Base-5 representation of 28 is 103; 1 + 0 + 3 = 4 divides 28.

MATHEMATICA

A064481Q[k_] := Divisible[k, DigitSum[k, 5]];

Select[Range[200], A064481Q] (* Paolo Xausa, May 03 2026 *)

PROG

(ARIBAS) maxarg := 160; for n := 1 to maxarg do if n mod sum(basearray(n, 5)) = 0 then write(n, " "); end; end; function basearray(n, b: integer): array; var k: integer; stk: stack; begin while n > 0 do k := n mod b; stack_push(stk, k); n := (n - k) div b; end; return stack2array(stk); end; .

(PARI) isok(n) = !(n % sumdigits(n, 5)); \\ Michel Marcus, Jun 24 2018

CROSSREFS

Cf. A049445 (base 2), A064150 (base 3), A064438 (base 4), A395676 (base 6), A395677 (base 7), A245802 (base 8), A395678 (base 9), A005349 (base 10).

Row 5 of A325309.

Cf. A344341.

Sequence in context: A003401 A281624 A242441 * A336505 A303704 A067939

Adjacent sequences: A064478 A064479 A064480 * A064482 A064483 A064484

KEYWORD

base,easy,nonn

AUTHOR

Klaus Brockhaus, Oct 03 2001

EXTENSIONS

Offset changed from 0 to 1 by Harry J. Smith, Sep 15 2009

STATUS

approved