Search: a323415 -id:a323415
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A323394
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Carryless sum of divisors of n.
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+10
3
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1, 3, 4, 7, 6, 2, 8, 5, 3, 18, 12, 18, 14, 14, 14, 11, 18, 19, 10, 32, 22, 36, 24, 30, 21, 32, 20, 36, 20, 52, 32, 43, 48, 44, 38, 51, 38, 40, 46, 70, 42, 76, 44, 74, 58, 62, 48, 84, 47, 83, 62, 88, 54, 80, 62, 80, 60, 70, 50, 48, 62, 96, 84, 7, 74, 24, 68, 6
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OFFSET
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1,2
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COMMENTS
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This sequence is a variant of A178910 for the base 10.
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LINKS
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FORMULA
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EXAMPLE
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For n = 42:
- the divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42,
- the sum of the units is: 1 + 2 + 3 + 6 + 7 + 4 + 1 + 2 = 26 == 6 (mod 10),
- the sum of the tens is: 1 + 2 + 4 = 7,
- hence a(42) = 76.
For n = 973:
- the divisors of 973 are: 1, 7, 139, 973,
- the sum of the units is: 1 + 7 + 9 + 3 = 20 == 0 (mod 10),
- the sum of the tens is: 3 + 7 = 10 == 0 (mod 10),
- the sum of the hundreds is: 1 + 9 = 10 == 0 (mod 10),
- hence a(973) = 0.
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MAPLE
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f:= proc(n) local t, d, dd, m, i;
t:= Vector(convert(n, base, 10));
for d in numtheory:-divisors(n) minus {n} do
dd:= convert(d, base, 10);
m:= nops(dd);
t[1..m]:= t[1..m] + Vector(dd) mod 10;
od:
add(t[i]*10^(i-1), i=1..ilog10(n)+1)
end proc:
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PROG
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(PARI) a(n, base=10) = my (v=[]); fordiv (n, d, my (w=Vecrev(digits(d, base))); v=vector(max(#v, #w), k, (if (k>#v, w[k], k>#w, v[k], (v[k]+w[k])%base)))); fromdigits(Vecrev(v), base)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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