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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: A051378 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

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Last modified April 17 21:31 EDT 2021. Contains 343070 sequences. (Running on oeis4.)