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%I A065925 #32 Jul 31 2021 05:53:52
%S A065925 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 A065925 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 A065925 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 A065925 Smallest k such that sopf(n+k) = sopf(k), where sopf = A008472.
%D A065925 J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 99-100. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 26 2009]
%H A065925 Harry J. Smith, <a href="/A065925/b065925.txt">Table of n, a(n) for n=1..1000</a>
%H A065925 Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_025.htm">Conjecture 25. sopf(n) = sopf(n+k)</a>, The Prime Puzzles and Problems Connection.
%e A065925 a(6) = 2 because A008472(2) = A008472(6+2) = 2, but A008472(1) = 0 doesn't equal A008472(6+1) = 7.
%t A065925 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 A065925 (PARI)
%o A065925 sopf(n) = local(fac, i); fac=factor(n); sum(i=1,matsize(fac)[1],fac[i,1])
%o A065925 A065925(m)={local(k,n); for(k=1,m,n=1; while(sopf(n)!=sopf(n+k), n++); print1(n,","))} \\ _Klaus Brockhaus_
%o A065925 (Python)
%o A065925 from sympy import primefactors
%o A065925 from itertools import count, dropwhile
%o A065925 def sopf(n): return sum(p for p in primefactors(n))
%o A065925 def a(n):
%o A065925   k = 1
%o A065925   while sopf(n+k) != sopf(k): k += 1
%o A065925   return k
%o A065925 print([a(n) for n in range(1, 77)]) # _Michael S. Branicky_, May 02 2021
%Y A065925 Cf. A008472, A065926, A065927.
%K A065925 nonn
%O A065925 1,1
%A A065925 _Jason Earls_, Nov 28 2001

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