|
|
A349628
|
|
Denominators of the Möbius transform of ratio A003961(n)/sigma(n).
|
|
6
|
|
|
1, 1, 4, 7, 6, 1, 8, 35, 52, 1, 12, 14, 14, 1, 24, 155, 18, 1, 20, 21, 32, 1, 24, 70, 186, 1, 104, 28, 30, 1, 32, 217, 48, 1, 16, 26, 38, 1, 56, 35, 42, 1, 44, 42, 312, 1, 48, 310, 456, 1, 72, 49, 54, 1, 72, 140, 80, 1, 60, 84, 62, 1, 416, 889, 28, 1, 68, 63, 96, 1, 72, 26, 74, 1, 744, 70, 32, 1, 80, 155, 968, 1, 84
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Because the ratio A003961(n)/A000203(n) is multiplicative, so is also its Möbius transform. This sequence gives the denominator of that ratio when presented in its lowest terms.
|
|
LINKS
|
|
|
MATHEMATICA
|
f[p_, e_] := NextPrime[p]^e*(p - 1)/(p^(e + 1) - 1); s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Denominator @ DivisorSum[n, s[#] * MoebiusMu[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 27 2021 *)
|
|
PROG
|
(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A349628(n) = denominator(sumdiv(n, d, moebius(n/d)*(A003961(d)/sigma(d))));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|