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A327166
Number of divisors d of n for which A000005(d)*d is equal to n, where A000005(x) gives the number of divisors of x.
9
1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1
OFFSET
1,108
COMMENTS
a(n) tells how many times in total n occurs in A038040.
LINKS
FORMULA
a(n) = Sum_{d|n} [A000005(d)*d == n], where [ ] is the Iverson bracket.
EXAMPLE
108 has the following twelve divisors: [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108]. Of these, only d=18 and d=27 are such that d*A000005(d) = 108, as 18*6 = 27*4 = 108. Thus a(108) = 2.
MATHEMATICA
Table[Sum[If[d*DivisorSigma[0, d] == n, 1, 0], {d, Divisors[n]}], {n, 1, 120}] (* Vaclav Kotesovec, Jul 23 2022 *)
PROG
(PARI) A327166(n) = sumdiv(n, d, (d*numdiv(d))==n);
CROSSREFS
Cf. also A327153, A327169.
Sequence in context: A067898 A010106 A096159 * A024155 A251570 A292241
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 19 2019
STATUS
approved