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 A257367 Composite numbers n equal to the sum of prime factors, counted with multiplicity, of the numbers in the interval [n-k,n+k], for some k. 5
 4, 75, 186, 531, 627, 5216, 22843, 148050, 1061385, 1490407, 1562485, 9034704, 10422738, 31920786, 76343543, 78824242, 105791155, 111873121, 131515163, 549038887, 1318856915, 1394579379, 1630428366, 1639063828, 3710476544, 3996221763, 4524478925, 6172721935 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime numbers are not considered because they are a trivial solution being the sum of their single prime factor (case k = 0). Composite n such that n = Sum_{i=-k..k} A001414(i+n) for some k. Values of k are 0, 1, 2, 4, 3, 4, 7, 6, 6, 8, 8, 9, 12, 8, 17, 9, 11, 4, 18, 11, ... LINKS Giovanni Resta, Table of n, a(n) for n = 1..40 (terms < 3*10^11) EXAMPLE Prime factors of 4 are 2, 2 and 2 + 2 = 4. In this case k = 0. For 75, k is equal to 1. Let us consider the prime factors of 74, 75 and 76. They are:  2, 37; 3, 5, 5; 2, 2, 19. Their sum is 2 + 37 + 3 + 5 + 5 + 2 + 2 + 19 = 75. For 186, k is equal to 2. Let us consider the prime factors of 184, 185, 186, 187, 188. They are: 2, 2, 2, 23; 5, 37; 2, 3, 31; 11, 17; 2, 2, 47. Their sum is 2 + 2 + 2 + 23 + 5 + 37 + 2 + 3 + 31 +  11 + 17 + 2 + 2 + 47 = 186. MAPLE with(numtheory); P:= proc(q) local a, c, d, j, k, n; for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; k:=0; a:=add(a[j][1]*a[j][2], j=1..nops(a)); while a

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Last modified May 17 21:11 EDT 2021. Contains 343990 sequences. (Running on oeis4.)