The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Antti Karttunen, Table of n, a(n) for n = 1..20000 Index entries for sequences computed from indices in prime factorization Index entries for sequences related to sigma(n) 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 Cf. A000203, A003961. Cf. A349627 (numerators). Cf. also A342671, A349161, A349162, A349634. Sequence in context: A354637 A173450 A200386 * A021025 A078974 A353668 Adjacent sequences: A349625 A349626 A349627 * A349629 A349630 A349631 KEYWORD nonn,frac AUTHOR Antti Karttunen, Nov 26 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 6 15:42 EDT 2024. Contains 374974 sequences. (Running on oeis4.)