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A351113
Sum of the balanced numbers dividing n.
3
1, 3, 4, 3, 1, 12, 1, 3, 4, 3, 1, 24, 1, 17, 19, 3, 1, 12, 1, 3, 4, 3, 1, 24, 1, 3, 4, 17, 1, 57, 1, 3, 4, 3, 36, 24, 1, 3, 4, 3, 1, 68, 1, 3, 19, 3, 1, 24, 1, 3, 4, 3, 1, 12, 1, 73, 4, 3, 1, 69, 1, 3, 4, 3, 1, 12, 1, 3, 4, 122, 1, 24, 1, 3, 19, 3, 1, 90, 1, 3, 4, 3, 1, 80
OFFSET
1,2
COMMENTS
A balanced number k is a number such that phi(k) | sigma(k).
LINKS
FORMULA
a(n) = Sum_{d|n, phi(d)|sigma(d)} d.
a(n) = Sum_{d|n} d * A351114(d).
a(n) = sigma(n) - Sum_{d|n} d * sign(sigma(d) mod phi(d)).
EXAMPLE
a(4) = 3; the balanced divisors of 4 are 1 and 2 and 1+2 = 3.
a(5) = 1; 1 is the only balanced divisor of 5.
a(6) = 12; the balanced divisors of 6 are 1,2,3,6 and 1+2+3+6 = 12.
MATHEMATICA
a[n_] := DivisorSum[n, # &, Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; Array[a, 100] (* Amiram Eldar, Feb 01 2022 *)
PROG
(PARI) a(n) = sumdiv(n, d, if (!(sigma(d) % eulerphi(d)), d)); \\ Michel Marcus, Feb 01 2022
CROSSREFS
Cf. A351112 (number of balanced divisors of n).
Cf. A000005 (tau), A000010 (phi), A000203 (sigma), A020492 (balanced numbers), A023897, A351114.
Sequence in context: A279676 A279588 A279590 * A201935 A225445 A167877
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 31 2022
STATUS
approved