来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a034448 Showing 1-1 of 1 %I A034448 %S A034448 1,3,4,5,6,12,8,9,10,18,12,20,14,24,24,17,18,30,20,30,32,36,24,36,26, %T A034448 42,28,40,30,72,32,33,48,54,48,50,38,60,56,54,42,96,44,60,60,72,48,68, %U A034448 50,78,72,70,54,84,72,72,80,90,60,120,62,96,80,65,84,144,68,90,96,144 %N A034448 usigma(n) = sum of unitary divisors of n (divisors d such that gcd(d, n/d)=1); also called UnitarySigma(n). %C A034448 Row sums of the triangle in A077610. - 2月12日,2002岁的C·A034 44 8乘以A(p^ e)=p^ e+1,E>0。---F.富兰克林·T·亚当斯-瓦特斯,9月11日2005n,a(n)n=1…10000的表%H A034 44 8 Steven R. Finch,统一论与无限论2004年2月25日。[缓存副本,作者的许可)〉%0H A034 44 8 Carl Pomerance和Hee Sung Yang,厄尔多斯关于有理因子函数和的一个定理的变式数学。CAMP,出现(2014).%%H A034 44 8 Tim Trudgian,酉因子函数的和《数学数学杂志》第2015卷第97期,第111期,第175-180.第0%H A034 44 8 Eric Weisstein的数学世界,酉除数函数%H A034 44维基百科酉因子%F A034 44,如果n=乘积Pi i^ Ei i,UsigMA(n)=乘积(pI i^ EaI+1)。4月19日,2001 V%的F A034 44 8 Dirichlet生成函数:ζ(S)*ζ(S-1)/Zeta(2S-1)。---F.富兰克林.T.AdAMS-瓦特斯,9月11日2005πF A034 44 8猜想:A(n)=sigma(n^ 2/rad(n))/sigma(n/rad(n)),其中sigma=a000 0203和rad=a00 7947。8月20日,2017‰E 12 A034 44 8酉因子为1, 3, 4,12。Or, 12=3*2^2 hence usigma(12)=(3+1)*(2^2+1)=20. %p A034448 A034448 := proc(n) local ans, i:ans := 1: for i from 1 to nops(ifactors(n)[ 2 ]) do ans := ans*(1+ifactors(n)[ 2 ][ i ][ 1 ]^ifactors(n)[ 2 ] [ i ] [ 2 ]): od: RETURN(ans) end: %p A034448 a := proc(n) local i; numtheory[divisors](n); select(d -> igcd(d,n/d)=1, %); add(i,i=%) end; # _Peter Luschny_, May 03 2009 %t A034448 usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; Table[ usigma[n], {n, 71}] (* _Robert G. Wilson v_, Aug 28 2004 *) %t A034448 Table[DivisorSum[n, # &, CoprimeQ[#, n/#] &], {n, 70}] (* _Michael De Vlieger_, Mar 01 2017 *) %t A034448 usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; Array[usigma, 100] (* faster since avoids generating divisors, _Giovanni Resta_, Apr 23 2017 *) %o A034448 (PARI) A034448(n)=sumdiv(n,d,if(gcd(d,n/d)==1,d)) \\ _Rick L. Shepherd_ %o A034448 (PARI) A034448(n) = {my(f=factorint(n)); prod(k=1, #f[,2], f[k,1]^f[k,2]+1)} \\ _Andrew Lelechenko_, 4月22日2014‰O A034 44 8(PARI)A(n)=SUMDEVMUT(N,D,IF(GCD(D,N/D)=1,D))·查尔R GraseSube IVI,SEP 09 2014 2014 %O A034 44 8(Haskell)A034 48= SUM。a077610_row -- _Reinhard Zumkeller_, Feb 12 2012 %Y A034448 Cf. A000203, A034444, A034460, A047994, A048250, A064000, A064609. %Y A034448 Cf. A063937 (squares > 1). %Y A034448 Cf. A188999, A301981, A301982. %K A034448 nonn,easy,nice,mult %O A034448 1,2 %A A034448 _N. J. A. Sloane_, Dec 11 1999 %E A034448 More terms from _Erich Friedman_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE