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A064807 Numbers which are divisible by their digital root (A010888). 8
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 19, 20, 21, 24, 27, 28, 30, 36, 37, 38, 39, 40, 42, 45, 46, 48, 50, 54, 55, 56, 57, 60, 63, 64, 66, 70, 72, 73, 74, 75, 76, 78, 80, 81, 82, 84, 90, 91, 92, 93, 95, 96, 99, 100, 102, 108, 109, 110, 111, 112, 114, 117, 118 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All numbers 9m, m > 0, belong to this sequence.

All numbers 6m, m > 0, belong to this sequence. - Christian Schulz, Oct 30 2013

All numbers 280m, m > 0, belong to this sequence. Only 6, 9, 280, and their multiples have this property. - Charles R Greathouse IV, Dec 26 2013

Conjecture: All k-multiply perfect numbers belong to this sequence. - Ivan N. Ianakiev, May 10 2016

LINKS

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

FORMULA

a(n) = a(n-1321) + 2520. - Charles R Greathouse IV, Dec 26 2013

EXAMPLE

48: 4 + 8 = 12 -> 1 + 2 = 3. 48 = 3 * 16 therefore 48 = a(28).

MAPLE

A064807 := proc(n) option remember: local k: if(n=1)then return 1:fi: for k from procname(n-1)+1 do if(k mod (((k-1) mod 9) + 1) = 0)then return k: fi: od: end: seq(A064807(n), n=1..100); # Nathaniel Johnston, May 05 2011

MATHEMATICA

Select[Range[125], Divisible[#, Mod[# - 1, 9] + 1] &] (* Alonso del Arte, Nov 01 2013 *)

PROG

(PARI) { n=0; for (m=1, 10^9, d=(m - 1)%9 + 1; if (m%d == 0, write("b064807.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Sep 26 2009

(PARI) is(n)=n%((n-1)%9+1)==0 \\ Charles R Greathouse IV, Dec 26 2013

(Haskell)

a064807 n = a064807_list !! (n-1)

a064807_list = filter (\x -> x `mod` a010888 x == 0) [1..]

-- Reinhard Zumkeller, Jan 03 2014

CROSSREFS

Cf. A010888.

Sequence in context: A180479 A193456 A143289 * A235591 A007603 A005349

Adjacent sequences:  A064804 A064805 A064806 * A064808 A064809 A064810

KEYWORD

nonn,base,easy

AUTHOR

Reinhard Zumkeller, Oct 21 2001

EXTENSIONS

Offset changed from 0 to 1, Harry J. Smith, Sep 26 2009

STATUS

approved

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Last modified February 21 14:39 EST 2018. Contains 299414 sequences. (Running on oeis4.)