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 A049060 a(n) = (-1)^omega(n)*Sum_{d|n} d*(-1)^omega(d), where omega(n) = A001221(n) is number of distinct primes dividing n. 23
 1, 1, 2, 5, 4, 2, 6, 13, 11, 4, 10, 10, 12, 6, 8, 29, 16, 11, 18, 20, 12, 10, 22, 26, 29, 12, 38, 30, 28, 8, 30, 61, 20, 16, 24, 55, 36, 18, 24, 52, 40, 12, 42, 50, 44, 22, 46, 58, 55, 29, 32, 60, 52, 38, 40, 78, 36, 28, 58, 40, 60, 30, 66, 125, 48, 20, 66, 80, 44, 24, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Might be called (-1)sigma(n). If x=Product p_i^r_i, then (-1)sigma(x)=Product (-1+Sum p_i^s_i, s_i=1 to r_i) = Product ((p_i^(r_i+1)-1)/(p_i-1)-2), with (-1)sigma(1)=1. - Yasutoshi Kohmoto, May 23 2005 Multiplicative with a(p^e) = (p^(e+1)-2*p+1)/(p-1). LINKS R. J. Mathar, Table of n, a(n) for n = 1..100000 FORMULA a(n) = Sum_{d|n} d*(-1)^A001221(d). MAPLE A049060 := proc(n) local it, ans, i, j; it := ifactors(n): ans := 1: for i from 1 to nops(ifactors(n)[2]) do ans := ans*(-1+sum(ifactors(n)[2][i][1]^j, j=1..ifactors(n)[2][i][2])): od: RETURN(ans) end: [seq(A049060(i), i=1..n)]; MATHEMATICA a[p_?PrimeQ] := p-1; a[1] = 1; a[n_] := Times @@ ((#[[1]]^(#[[2]] + 1) - 2*#[[1]] + 1)/(#[[1]] - 1) & ) /@ FactorInteger[n]; Table[a[n], {n, 1, 71}] (* Jean-François Alcover, May 21 2012 *) PROG (PARI) A049060(n)={ local(i, resul, rmax, p) ; if(n==1, return(1) ) ; i=factor(n) ; rmax=matsize(i)[1] ; resul=1 ; for(r=1, rmax, p=0 ; for(j=1, i[r, 2], p += i[r, 1]^j ; ) ; resul *= p-1 ; ) ; return(resul) ; } { for(n=1, 40, print(n, " ", A049060(n)) ) ; } \\ R. J. Mathar, Oct 12 2006 CROSSREFS Used in A049057, A049058, A049059. Cf. A000203, A057723, A060640, A126602, A126690. Sequence in context: A177067 A055127 A152669 * A092462 A256357 A160826 Adjacent sequences:  A049057 A049058 A049059 * A049061 A049062 A049063 KEYWORD easy,nonn,nice,mult AUTHOR EXTENSIONS More terms from James A. Sellers, May 03 2000 Better description from Vladeta Jovovic, Apr 06 2002 STATUS approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)