

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


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. AdamsWatters, Aug 24 2013


STATUS

approved



