A347124 Möbius transform of A341528, n * sigma(A003961(n)).

1, 7, 17, 44, 39, 119, 83, 268, 261, 273, 153, 748, 233, 581, 663, 1616, 339, 1827, 455, 1716, 1411, 1071, 689, 4556, 1385, 1631, 3933, 3652, 927, 4641, 1177, 9712, 2601, 2373, 3237, 11484, 1553, 3185, 3961, 10452, 1803, 9877, 2063, 6732, 10179, 4823, 2537, 27472, 6433, 9695, 5763, 10252, 3179, 27531, 5967, 22244

Offset

1,2

Comments

Multiplicative because A341528 is.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = Sum_{d|n} A008683(n/d) * A341528(d).

a(n) = A347125(n) - A346239(n).

Multiplicative with a(p^e) = p^(e-1)*(q^e*(p*q-1)-p+1)/(q-1), where q = A151800(p). - Sebastian Karlsson, Sep 02 2021

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A003973(n) = sigma(A003961(n));
A341528(n) = (n*A003973(n));
A347124(n) = sumdiv(n, d, moebius(n/d)*A341528(d));

Crossrefs

Cf. A003961, A003973, A008683, A151800, A341528, A341512, A346239, A347125.

Sequence in context: A124965 A253973 A200080 * A179030 A179031 A107178

Adjacent sequences: A347121 A347122 A347123 * A347125 A347126 A347127

Keyword

nonn,mult

Author

Antti Karttunen, Aug 24 2021

Status

approved