A355416 a(n) is the least k such that k divides Sum_{i=k..k+n-1} A001414(i).

1, 1, 2, 6, 12, 3, 6, 1, 2, 22, 7, 11, 3, 25, 13, 15, 9, 1, 25, 5, 5, 10, 26, 22, 69, 1, 1, 34, 42, 73, 41, 28, 54, 130, 99, 11, 14, 8, 34, 64, 84, 27, 62, 21, 28, 15, 102, 4, 36, 104, 48, 24, 1, 31, 17, 38, 44, 5, 183, 2, 6, 37, 222, 13, 27, 16, 156, 44, 35, 16, 26, 101, 36, 45, 70, 37, 21, 70

Offset

1,3

Comments

a(n) is the least k such that k divides the sum with multiplicities of the prime factors of the n numbers starting with k.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4) = 6 because the 4 numbers starting with 6 are 6=2*3, 7, 8=2^3, 9=3^2, and 2+3+7+2+2+2+3+3 = 24 is divisible by 4, and no number less than 6 works.

Maple

spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
S:= map(spf, [$1..10^6]):
SS:= ListTools:-PartialSums(S):
f:= proc(n) local t, i;
    if SS[n] mod n = 0 then return 1 fi;
    for i from 2 to 10^6-n do
      if SS[i+n-1]-SS[i-1] mod n = 0 then return i fi;
    od;
    -1
end proc:
map(f, [$1..100]);

Crossrefs

Cf. A001414.

Sequence in context: A293122 A014452 A188894 * A054579 A277962 A209386

Adjacent sequences: A355413 A355414 A355415 * A355417 A355418 A355419

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 01 2022

Status

approved