

A080737


a(1)=a(2)=0, a(2^r) = phi(2^r) (r>1), a(p^r) = phi(p^r) (p odd prime, r>=1), where phi is Euler's function A000010 and in general if n = Product p_i^e_i, a(n) = Sum a(p_i^e_i).


8



0, 0, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 6, 8, 16, 6, 18, 6, 8, 10, 22, 6, 20, 12, 18, 8, 28, 6, 30, 16, 12, 16, 10, 8, 36, 18, 14, 8, 40, 8, 42, 12, 10, 22, 46, 10, 42, 20, 18, 14, 52, 18, 14, 10, 20, 28, 58, 8, 60, 30, 12, 32, 16, 12, 66, 18, 24, 10, 70, 10, 72, 36, 22, 20, 16, 14
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OFFSET

1,3


REFERENCES

J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202209.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


MATHEMATICA

a[1] = a[2] = 0; a[p_?PrimeQ] := a[p] = p1; a[n_] := a[n] = If[Length[fi = FactorInteger[n]] == 1, EulerPhi[n], Total[a /@ (fi[[All, 1]]^fi[[All, 2]])]]; Table[a[n], {n, 1, 78}] (* JeanFrançois Alcover, Jun 20 2012 *)


PROG

(PARI) {for(n=1, 78, k=0; if(n>1, f=factor(n); k=sum(j=1, matsize(f)[1], eulerphi(f[j, 1]^f[j, 2])); if(f[1, 1]==2&&f[1, 2]==1, k)); print1(k, ", "))}
(Haskell)
a080737 n = a080737_list !! (n1)
a080737_list = 0 : (map f [2..]) where
f n  mod n 4 == 2 = a080737 $ div n 2
 otherwise = a067240 n
 Reinhard Zumkeller, Jun 13 2012, Jun 11 2012


CROSSREFS

Cf. A080736, A080738, A080739, A080740, A067240.
See A152455 for another version.
Cf. S067240, A000010, A141809.
Sequence in context: A096504 A011773 * A152455 A000010 A003978 A122645
Adjacent sequences: A080734 A080735 A080736 * A080738 A080739 A080740


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Mar 08 2003


EXTENSIONS

More terms and PARI code from Klaus Brockhaus, Mar 10 2003


STATUS

approved



