A109353 a(n) is the sum of the distinct prime divisors of A024619(n).
5, 7, 5, 9, 8, 5, 7, 10, 13, 5, 15, 9, 10, 14, 19, 12, 5, 21, 16, 7, 12, 13, 8, 25, 5, 7, 20, 15, 5, 16, 9, 22, 31, 10, 33, 10, 18, 16, 19, 26, 14, 5, 39, 8, 21, 18, 18, 7, 43, 12, 22, 45, 32, 13, 10, 20, 25, 34, 49, 24, 5, 9, 14, 7, 22, 15, 15, 55, 5, 18, 40, 9, 24, 28, 31, 16, 61, 24
Offset: 1
Examples
a(3)=5 because the 3rd non-prime-power is 12 and its prime factors sum to 5.
Crossrefs
Cf. A024619.
Programs
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PARI
distinct(n) = \sum the distinct prime factors of n { local(a,x,m,ln,s); for(m=2,n, s=0; a=ifactord(m); ln=length(a); if(ln > 1, for(x=1,ln, s+=a[x]; ); print1(s",") ) ) } ifactord(n,m=0) = \distinct prime factors of n { local(f,j,k,flist); flist=[]; f=Vec(factor(n,m)); for(j=1,length(f[1]), flist = concat(flist,f[1][j]) ); return(flist) }
Extensions
Edited by Don Reble, Jul 23 2006