A034690 Sum of digits of all the divisors of n.

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, 29, 12, 27, 5, 27, 12, 18, 21, 46, 11, 24, 20, 27, 6, 33, 8, 21, 33, 18, 12, 52, 21, 21, 18, 26, 9, 48, 18, 48, 26, 27, 15, 42, 8, 15, 32, 37, 21, 36, 14, 36, 24, 36, 9, 69, 11, 24, 34

Offset

1,2

Comments

For first occurrence of k, or 0 if k never appears, see A191000.

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

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

H. Havermann et al, in reply to E. Angelini, List the dividers, sum the digits, SeqFan list, Nov. 2015.

Maxwell Schneider and Robert Schneider, Digit sums and generating functions, arXiv:1807.06710 [math.NT], 2018-2020. See (22) p. 6.

Example

a(15) = 1 + 3 + 5 + (1+5) = 15. - M. F. Hasler, Nov 08 2015

Maple

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;
# Alternative:
sd:= proc(n) option remember; local k; k:= n mod 10; k + procname((n-k)/10) end proc:
for n from 0 to 9 do sd(n):= n od:
a:= n -> add(sd(d), d=numtheory:-divisors(n)):
map(a, [$1..100]); # Robert Israel, Nov 17 2015

Mathematica

Table[Plus @@ Flatten@ IntegerDigits@ Divisors@n, {n, 75}] (* Robert G. Wilson v, Sep 30 2006 *)

Prog

(Haskell)
a034690 = sum . map a007953 . a027750_row
-- Reinhard Zumkeller, Jan 20 2014
(PARI) vector(100, n, sumdiv(n, d, sumdigits(d))) \\ Michel Marcus, Jun 28 2015
(PARI) A034690(n)=sumdiv(n, d, sumdigits(d)) \\ For use in other sequences. - M. F. Hasler, Nov 08 2015
(Python)
from sympy import divisors
def sd(n): return sum(map(int, str(n)))
def a(n): return sum(sd(d) for d in divisors(n))
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Oct 06 2021

Crossrefs

Cf. A000005, A000203, A007953, A086793, A191000.

Cf. A093653 (binary equivalent)

Sequence in context: A088000 A284344 A168338 * A069192 A076887 A351395

Adjacent sequences: A034687 A034688 A034689 * A034691 A034692 A034693

Keyword

base,easy,nonn

Author

Erich Friedman

Status

approved