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%I #49 Jan 02 2023 12:30:46
%S 1,3,4,7,6,12,8,15,13,9,3,19,5,15,15,22,9,30,11,15,14,9,6,33,13,15,22,
%T 29,12,27,5,27,12,18,21,46,11,24,20,27,6,33,8,21,33,18,12,52,21,21,18,
%U 26,9,48,18,48,26,27,15,42,8,15,32,37,21,36,14,36,24,36,9,69,11,24,34
%N Sum of digits of all the divisors of n.
%C For first occurrence of k, or 0 if k never appears, see A191000.
%C The only fixed points are 1 and 15. These are also the only loops of iterations of A034690: see the SeqFan thread "List the divisors...". - _M. F. Hasler_, Nov 08 2015
%C The following sequence is composed of numbers n such that the sum of digits of all divisors of n equals 15: 8, 14, 15, 20, 26, 59, 62, ... It actually depicts the positions of number 15 in this sequence: see the SeqFan thread "List the divisors...". - _V.J. Pohjola_, Nov 09 2015
%H Reinhard Zumkeller, <a href="/A034690/b034690.txt">Table of n, a(n) for n = 1..10000</a>
%H H. Havermann et al, in reply to E. Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2015-November/015581.html">List the dividers, sum the digits</a>, SeqFan list, Nov. 2015.
%H Maxwell Schneider and Robert Schneider, <a href="https://arxiv.org/abs/1807.06710">Digit sums and generating functions</a>, arXiv:1807.06710 [math.NT], 2018-2020. See (22) p. 6.
%e a(15) = 1 + 3 + 5 + (1+5) = 15. - _M. F. Hasler_, Nov 08 2015
%p with(numtheory); read transforms; f:=proc(n) local t1, t2, i; t1:=divisors(n); t2:=0; for i from 1 to nops(t1) do t2:=t2+digsum(t1[i]); od: t2; end;
%p # Alternative:
%p sd:= proc(n) option remember; local k; k:= n mod 10; k + procname((n-k)/10) end proc:
%p for n from 0 to 9 do sd(n):= n od:
%p a:= n -> add(sd(d), d=numtheory:-divisors(n)):
%p map(a, [$1..100]); # _Robert Israel_, Nov 17 2015
%t Table[Plus @@ Flatten@ IntegerDigits@ Divisors@n, {n, 75}] (* _Robert G. Wilson v_, Sep 30 2006 *)
%o (Haskell)
%o a034690 = sum . map a007953 . a027750_row
%o -- _Reinhard Zumkeller_, Jan 20 2014
%o (PARI) vector(100, n, sumdiv(n, d, sumdigits(d))) \\ _Michel Marcus_, Jun 28 2015
%o (PARI) A034690(n)=sumdiv(n,d,sumdigits(d)) \\ For use in other sequences. - _M. F. Hasler_, Nov 08 2015
%o (Python)
%o from sympy import divisors
%o def sd(n): return sum(map(int, str(n)))
%o def a(n): return sum(sd(d) for d in divisors(n))
%o print([a(n) for n in range(1, 76)]) # _Michael S. Branicky_, Oct 06 2021
%Y Cf. A000005, A000203, A007953, A086793, A191000.
%Y Cf. A093653 (binary equivalent)
%K base,easy,nonn
%O 1,2
%A _Erich Friedman_
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