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A354992
Number of divisors d of n for which A344005(d) < A344005(n), where A344005(n) is the smallest positive integer m such that n divides m*(m+1).
4
0, 0, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 3, 4, 1, 4, 1, 3, 2, 2, 1, 7, 2, 2, 3, 5, 1, 6, 1, 5, 3, 2, 3, 6, 1, 2, 2, 7, 1, 4, 1, 5, 5, 2, 1, 8, 2, 4, 3, 3, 1, 6, 2, 5, 2, 2, 1, 11, 1, 2, 5, 6, 3, 6, 1, 3, 3, 6, 1, 7, 1, 2, 4, 5, 3, 4, 1, 7, 4, 2, 1, 11, 3, 2, 3, 7, 1, 10, 3, 5, 2, 2, 3, 11, 1, 4, 5, 6, 1, 6, 1, 7, 6
OFFSET
1,4
LINKS
FORMULA
a(n) = Sum_{d|n} [A344005(d) < A344005(n)], where [ ] is the Iverson bracket.
a(n) = A000005(n) - A354991(n).
MAPLE
g:= proc(n) option remember; local t, x;
min(map(t -> rhs(op(t)), {msolve(x*(x+1), n)}) minus {0})
end proc:
g(1):= 1: g(2):= 1:
f:= proc(n) local d, v;
v:= g(n);
nops(select(t -> g(t) < v, numtheory:-divisors(n)))
end proc:
map(f, [$1..100]); # Robert Israel, Jun 17 2022
MATHEMATICA
s[n_] := Module[{m = 1}, While[! Divisible[m*(m + 1), n], m++]; m]; a[n_] := Module[{sn = s[n]}, DivisorSum[n, 1 &, # < n && s[#] < sn &]]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)
PROG
(PARI)
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354992(n) = { my(x=A344005(n)); sumdiv(n, d, A344005(d)<x); };
CROSSREFS
Cf. also A344589, A345936.
Sequence in context: A337093 A320266 A277692 * A129138 A353378 A112970
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 17 2022
STATUS
approved