A287923 Numbers equal to the sum of the prime factors, with multiplicity, of the previous and of the following k numbers, for some k.

260, 3100, 4699, 29318, 54760, 82952, 315657, 380741, 574883, 873815, 949282, 1766959, 2114033, 3971361, 5418111, 6972931, 7644772, 9714402, 15752927, 30118112, 91750525, 129381240, 130672476, 395713882, 450192670, 523370293, 553444691, 833889991

Offset

1,1

Comments

Similar to A257367 but here the prime factors of a(n) are not considered.

Again, while in A257367 the prime numbers are not allowed because they would be just a trivial solution, here they are part of the terms of the sequence. The first one is 15752927.

Values of k are 2, 2, 3, 6, 4, 7, 5, 4, 7, 8, 11, 11, 5, 8, 11, 11, 9, 5, 9, 15, 14, 7, 9, 10, 12, 17, 19, 33, ...

Numbers tested up to 10^9.

Links

Giovanni Resta, Table of n, a(n) for n = 1..40

Formula

x = Sum_{i = -k..k} A001414(i+x) - A001414(x), for some k.

Example

258 = 2*3*43, 259 = 7*37, 261 = 3*3*29, 262 = 2*131 and 2 + 3 + 43 + 7 + 37 + 3 + 3 + 29 + 2 + 131 = 260.

Maple

with(numtheory): P:= proc(q) local a, b, c, k, n;
for n from 1 to q do a:=0; k:=0; while a<n do k:=k+1;
b:=ifactors(n-k)[2]; b:=add(b[j][1]*b[j][2], j=1..nops(b));
c:=ifactors(n+k)[2]; c:=add(c[j][1]*c[j][2], j=1..nops(c));
a:=a+b+c; od; if a=n then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A001414, A257367, A257524, A257525, A257929, A257930, A257976.

Sequence in context: A061224 A108109 A235905 * A238029 A264254 A254647

Adjacent sequences: A287920 A287921 A287922 * A287924 A287925 A287926

Keyword

nonn

Author

Paolo P. Lava, Jun 15 2017

Status

approved