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A349170
a(n) = Sum_{d|n} d * A003959(n/d), where A003959 is fully multiplicative with a(p) = (p+1).
7
1, 5, 7, 19, 11, 35, 15, 65, 37, 55, 23, 133, 27, 75, 77, 211, 35, 185, 39, 209, 105, 115, 47, 455, 91, 135, 175, 285, 59, 385, 63, 665, 161, 175, 165, 703, 75, 195, 189, 715, 83, 525, 87, 437, 407, 235, 95, 1477, 169, 455, 245, 513, 107, 875, 253, 975, 273, 295, 119, 1463, 123, 315, 555, 2059, 297, 805, 135, 665
OFFSET
1,2
COMMENTS
Dirichlet convolution of A003959 with the identity function, A000027.
Dirichlet convolution of sigma (A000203) with A003968.
LINKS
FORMULA
a(n) = Sum_{d|n} d * A003959(n/d).
a(n) = Sum_{d|n} A349171(d).
a(n) = Sum_{d|n} A000203(d) * A003968(n/d).
a(n) = A038040(n) + A349140(n).
For all n >= 1, a(n) >= A349129(n) >= A349130(n).
Multiplicative with a(p^e) = (p+1)^(e+1) - p^(e+1). - Amiram Eldar, Nov 09 2021
MATHEMATICA
f[p_, e_] := (p + 1)^(e + 1) - p^(e + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 09 2021 *)
PROG
(PARI)
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A349170(n) = sumdiv(n, d, d*A003959(n/d));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 09 2021
STATUS
approved