The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A107749 OrdinaryUnitarySigma(n): If n = Product p_i^r_i then OUSigma(n) = Sigma(2^r_1)*UnitarySigma(n/2^r_1). 5
 1, 3, 4, 7, 6, 12, 8, 15, 10, 18, 12, 28, 14, 24, 24, 31, 18, 30, 20, 42, 32, 36, 24, 60, 26, 42, 28, 56, 30, 72, 32, 63, 48, 54, 48, 70, 38, 60, 56, 90, 42, 96, 44, 84, 60, 72, 48, 124, 50, 78, 72, 98, 54, 84, 72, 120, 80, 90, 60, 168, 62, 96, 80, 127, 84, 144, 68, 126, 96 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000203(p2) * A034448(n/p2), where p2 = A006519(n). - R. J. Mathar, Jun 15 2008 Multiplicative with a(2^e) = 2^(e+1)-1, a(p^e) = p^e+1 for p>2, e>0. EXAMPLE OUSigma(2^4*7^2) = Sigma(2^4)*UnitarySigma(7^2) = 31*50 = 1550. MAPLE A107749 := proc(n) local a, f, p, e; a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; if p = 2 then a := a*(2^(e+1)-1) ; else a := a*(p^e+1) ; end if; end do; a ; end proc: # R. J. Mathar, Jun 02 2011 MATHEMATICA f[2, e_] := 2^(e+1)-1; f[p_, e_] := p^e+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 15 2020 *) PROG (PARI) a(n)=local(fm); fm=factor(n); prod(k=1, matsize(fm)[1], if(fm[k, 1]==2, 2^(fm[k, 2]+1)-1, fm[k, 1]^fm[k, 2]+1)) CROSSREFS Cf. A069184, A091321, A000203, A034448, A006519. Sequence in context: A344575 A254981 A116607 * A093811 A088000 A284344 Adjacent sequences:  A107746 A107747 A107748 * A107750 A107751 A107752 KEYWORD nonn,mult AUTHOR Yasutoshi Kohmoto, Jun 11 2005, Feb 24 2007 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007 More terms from R. J. Mathar, Jun 15 2008 Name corrected by Franklin T. Adams-Watters, Aug 24 2013 STATUS approved

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

Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)