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Robert Israel, <a href="/A146754/b146754_1.txt">Table of n, a(n) for n = 1..258</a>
f:= proc(d) # solutions with d+1 digits
local b, R, a;
R:= NULL;
for b from ceil(49*10^(d-1)/(10^d - 1)) to 9 do
a:= (10^d-5)*b/49;
if a::integer then R:= R, 10*a+b fi
od;
R
end proc:
map(f, [$1..42]); # Robert Israel, Nov 05 2024
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Includes all terms > 5 of A077497. - Robert Israel, Nov 05 2024
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A prime p > 5 is here if the multiplicative order of 10 (mod p) is of the form 2^i*5^j, with i and j nonnegative.
Robert Israel, <a href="/A178070/b178070_1.txt">Table of n, a(n) for n = 1..110</a>
filter:= proc(p) local v;
if not isprime(p) then return false fi;
v:= numtheory:-order(10, p);
v = 2^padic:-ordp(v, 2) * 5^padic:-ordp(v, 5)
end proc:
select(filter, [seq(i, i=7 .. 10^6, 2)]); # Robert Israel, Nov 05 2024
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Robert Israel, <a href="/A198302/b198302_1.txt">Table of n, a(n) for n = 1..6236</a>
f:= proc(n) local d; add(d*numtheory:-sigma[d](n/d), d=numtheory:-divisors(n)) end proc:
map(f, [$1..100]); # Robert Israel, Nov 05 2024
nonn,look
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Robert Israel, <a href="/A071825/a071825.png">Log-log plot of (n, a(n)) for 1 <= n <= 10^6</a>