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A338171
a(n) is the sum of those divisors d of n such that tau(d) divides sigma(d).
4
1, 1, 4, 1, 6, 10, 8, 1, 4, 6, 12, 10, 14, 22, 24, 1, 18, 10, 20, 26, 32, 34, 24, 10, 6, 14, 31, 22, 30, 60, 32, 1, 48, 18, 48, 10, 38, 58, 56, 26, 42, 94, 44, 78, 69, 70, 48, 10, 57, 6, 72, 14, 54, 91, 72, 78, 80, 30, 60, 140, 62, 94, 32, 1, 84, 142, 68, 86
OFFSET
1,3
COMMENTS
a(n) is the sum of arithmetic divisors d of n.
a(n) = sigma(n) = A000203(n) for numbers n from A334420.
See A338170 and A338172 for number and product such divisors.
LINKS
FORMULA
a(p) = p + 1 for odd primes p (A065091).
EXAMPLE
a(6) = 10 because there are 3 arithmetic divisors of 6 (1, 3 and 6): sigma(1)/tau(1) = 1/1 = 1; sigma(3)/tau(3) = 4/2 = 2; sigma(6)/tau(6) = 12/4 = 3. Sum of this divisors is 10.
MAPLE
f:= proc(n) uses numtheory;
convert(select(t -> sigma(t) mod tau(t) = 0, divisors(n)), `+`) end proc:
map(f, [$1..100]); # Robert Israel, Oct 27 2020
MATHEMATICA
a[n_] := DivisorSum[n, # &, Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &]; Array[a, 100] (* Amiram Eldar, Oct 15 2020 *)
PROG
(Magma) [&+[d: d in Divisors(n) | IsIntegral(&+Divisors(d) / #Divisors(d))]: n in [1..100]];
(PARI) a(n) = sumdiv(n, d, d*!(sigma(d) % numdiv(d))); \\ Michel Marcus, Oct 15 2020
CROSSREFS
Cf. A000005 (tau), A000203 (sigma), A003601 (arithmetic numbers).
Sequence in context: A122662 A210228 A209161 * A333824 A083843 A094264
KEYWORD
nonn,look
AUTHOR
Jaroslav Krizek, Oct 14 2020
STATUS
approved