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A065925 Smallest k such that sopf(n+k) = sopf(k), where sopf = A008472. 5

%I

%S 5,2,7,4,114,2,5,8,13,10,25,4,5,2,19,16,85,6,5,5,209,22,25,3,493,26,

%T 31,4,20,2,5,32,7,34,516,12,33,38,10,10,99,6,5,44,57,46,25,6,5,50,49,

%U 52,52,18,855,8,61,58,295,4,261,2,91,64,602,6,5,68,21,10,25,9,7,74,13,76

%N Smallest k such that sopf(n+k) = sopf(k), where sopf = A008472.

%D J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 99-100. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 26 2009]

%H Harry J. Smith, <a href="/A065925/b065925.txt">Table of n, a(n) for n=1..1000</a>

%H C. Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_025.htm">www.primepuzzles.net, Conjecture 25</a>

%e a(6) = 2 because A008472(2) = A008472(6+2) = 2, but A008472(1) = 0 doesn't equal A008472(6+1) = 7.

%t Table[k = 1; While[Total[FactorInteger[n + k][[All, 1]]] != Total[FactorInteger[k][[All, 1]]], k++]; k, {n, 76}] (* _Michael De Vlieger_, Jan 11 2017 *)

%o (PARI) sopf(n) = local(fac, i); fac=factor(n); sum(i=1,matsize(fac)[1],fac[i,1]) A065925(m)={local(k,n); for(k=1,m,n=1; while(sopf(n)!=sopf(n+k), n++); print1(n,","))} \\ _Klaus Brockhaus_

%o (PARI) sopf(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) } { for (n=1, 1000, k=2; while (sopf(n + k) != sopf(k), k++); write("b065925.txt", n, " ", k) ) } \\ _Harry J. Smith_, Nov 04 2009

%Y Cf. A008472, A065926, A065927.

%K nonn

%O 1,1

%A _Jason Earls_, Nov 28 2001

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Last modified August 13 02:52 EDT 2020. Contains 336441 sequences. (Running on oeis4.)