Search: id:A112264
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%I A112264
%S A112264 0,2,3,4,5,6,7,6,6,7,1,7,1,9,8,8,1,8,1,9,10,3,2,9,10,3,9,11,2,10,3,10,
               4,
%T A112264 3,8,10,3,3,4,11,4,12,4,5,11,4,4,11,14,12,4,5,5,11,6,13,4,4,5,12,6,5,13,
%U A112264 12,6,6,6,5,5,14,7,12,7,5,13,5,8,6,7,13,12,6,8,14,6,6,5,7,8,13,8,6,6,6
%N A112264 Sum of initial digits of prime factors (with multiplicity) of n.
%C A112264 For primes p, elements of A000040, a(p) = A000030(p). The cumulative 
               sum of this sequence is A112265. Primes in the cumulative sum are 
               A112266. This is a base 10 sequence, the base 1 equivalent is A001222(n) 
               = BigOmega(n) = e_1 + e_2 + ... + e_k, the number of prime factors 
               (with multiplicity), where k = A001221(n) = SmallOmega(n). The base 
               2 equivalent is equal to the base 1 equivalent. The base 3 equivalent 
               is A112267, base 4 is A112268, base 5 is A112269, base 6 is A112270, 
               base 7 is A112271, base 8 is A112272, base 9 is A112273.
%H A112264 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeFactor.html">Prime Factor.</a>
%H A112264 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DistinctPrimeFactors.html">Distinct Prime Factors.</a>
%F A112264 a(1) = 0 and given the prime factorization n = (p_1)^(e_1) * (p_2)^(e_2) 
               * ... * (p_k)^(e_k) then a(n) = (e_1)*A000030(p_1) + (e_2)*A000030(p_2) 
               + ... + (e_k)*A000030(p_l).
%e A112264 a(4) = 4 because 4 = 2*2, so the sum of the initial digits is 2 + 2 = 
               4.
%e A112264 a(11) = 1 because 11 is prime and its initial digit is 1.
%e A112264 a(22) = 3 because 22 = 2*11, so the sum of the initial digits is 2 + 
               1 = 3.
%e A112264 a(98) = 16 because 98 = 2 * 7^2, so the sum of the initial digits is 
               2 + 7 + 7 = 16.
%e A112264 a(100) = 14 because 100 = 2^2 * 5^2, so the sum of the initial digits 
               is 2 + 2 + 5 + 5 = 14.
%e A112264 a(121) = 2 because 121 = 11^2, so the sum of the initial digits is 1 
               + 1 = 2.
%e A112264 a(361) = 2 because 361 = 19^2, so the sum of the initial digits is 1 
               + 1 = 2.
%Y A112264 Cf. A000030, A000040, A001221, A001222, A112266-A112273.
%Y A112264 Sequence in context: A073794 A017892 A017882 this_sequence A017872 A161209 
               A000026
%Y A112264 Adjacent sequences: A112261 A112262 A112263 this_sequence A112265 A112266 
               A112267
%K A112264 base,easy,nonn
%O A112264 1,2
%A A112264 Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 30 2005

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