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A064351 Numbers n such that n and n+1 have the same sum and number of prime divisors (with repetition). 1

%I #15 Dec 15 2017 17:35:38

%S 6867,57075,113283,155708,230124,244035,250995,351075,437715,508563,

%T 667628,742508,1065843,1095315,1166067,1302092,1379907,1431212,

%U 1496780,2373452,2519343,2978787,2992220,3164524,3583772,4799011,4826835,5103875,5140316,5535404

%N Numbers n such that n and n+1 have the same sum and number of prime divisors (with repetition).

%H Harry J. Smith and Donovan Johnson, <a href="/A064351/b064351.txt">Table of n, a(n) for n = 1..1000</a> (first 80 terms from Harry J. Smith)

%t snpd[n_]:=Module[{fi=FactorInteger[n]},{Total[Flatten[Table[#[[1]],{#[[2]]}]&/@fi]],Total[Transpose[fi][[2]]]}]; Flatten[Position[Partition[ Array[ snpd,5600000],2,1],_?(#[[1]]==#[[2]]&),{1},Heads->False]] (* _Harvey P. Dale_, Nov 29 2013 *)

%o (PARI) sopfr(n)= { local(c,f,s=0); G=0; f=factor(n); for(i=1, matsize(f)[1], c=f[i, 2]; G+=c; s+=f[i, 1]*c); return(s) } { n=c=s=0; for (m=1, 10^9, us=sopfr(m + 1); if(c==G && s==us, write("b064351.txt", n++, " ", m); if (n==100, break)); c=G; s=us ) } \\ _Harry J. Smith_, Sep 12 2009

%Y Cf. A001414, A001222.

%K nonn

%O 1,1

%A _Jason Earls_, Oct 15 2001

%E a(25) - a(27) from _Harry J. Smith_, Sep 12 2009

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