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A349171 a(n) = Sum_{d|n} phi(d) * A003959(n/d), where A003959 is fully multiplicative with a(p) = (p+1), and phi is Euler totient function. 7
1, 4, 6, 14, 10, 24, 14, 46, 30, 40, 22, 84, 26, 56, 60, 146, 34, 120, 38, 140, 84, 88, 46, 276, 80, 104, 138, 196, 58, 240, 62, 454, 132, 136, 140, 420, 74, 152, 156, 460, 82, 336, 86, 308, 300, 184, 94, 876, 154, 320, 204, 364, 106, 552, 220, 644, 228, 232, 118, 840, 122, 248, 420, 1394, 260, 528, 134, 476, 276 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Dirichlet convolution of A003959 with Euler totient function phi, A000010.
Möbius transform of A349170.
LINKS
FORMULA
a(n) = Sum_{d|n} A000010(d) * A003959(n/d).
a(n) = Sum_{d|n} A008683(d) * A349170(n/d).
a(n) = Sum_{k=1..n} A003959(gcd(n, k)).
a(n) = A018804(n) + A349141(n).
For all n >= 1, a(n) >= A349131(n).
Multiplicative with a(p^e) = p*(p+1)^e - (p-1)*p^e. - Amiram Eldar, Nov 09 2021
MATHEMATICA
f[p_, e_] := p*(p + 1)^e - (p - 1)*p^e; 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); };
A349171(n) = sumdiv(n, d, eulerphi(d)*A003959(n/d));
CROSSREFS
Cf. A000010, A003959, A018804, A349141, A349170 (inverse Möbius transform), A349172, A349131.
Sequence in context: A365963 A095867 A253535 * A338658 A344224 A310601
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 09 2021
STATUS
approved

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)