

A274010


Boris Stechkin function: a(n) is the number of m with 2 <= m <= n and floor(n(m1)/m) divisible by m1.


1



0, 0, 1, 2, 3, 3, 4, 4, 4, 5, 5, 4, 6, 6, 4, 6, 7, 5, 6, 6, 6, 8, 6, 4, 8, 9, 5, 6, 8, 6, 8, 8, 6, 8, 6, 6, 11, 9, 4, 6, 10, 8, 8, 8, 6, 10, 8, 4, 10, 11, 7, 8, 8, 6, 8, 10, 10, 10, 6, 4, 12, 12, 4, 8, 11, 9, 10, 8, 6, 8, 10, 8, 12, 12, 4, 8, 10, 8, 10, 8, 10
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OFFSET

0,4


COMMENTS

Stechkin proves:
n1 is prime iff a(n) = A000005(n).
n1 and n+1 are twin primes, i.e. n is in A014574, iff a(n)+a(n+1) = A000005(n).
If p < q are odd primes, then Sum_{k=p+1..q} (1)^k a(k) = 0.


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, Springer 2013, sec. A17.


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000


EXAMPLE

For n = 6, the values of m are 2,3,5,6 so a(6) = 4.


MAPLE

N:= 1000: # to get a(0) to a(N)
A:= Vector(N):
for m from 2 to N do
L:= [seq(seq(k*m+j, j=0..1), k=1..N/m)];
if L[1] > N then L:= L[1..2] fi;
A[L]:= map(`+`, A[L], 1);
od:
0, seq(A[i], i=1..N);


PROG

(PARI) a(n)=sum(m=2, n, n*(m1)\m%(m1)==0) \\ Charles R Greathouse IV, Jun 08 2016


CROSSREFS

Cf. A000005, A014574, A055004.
Sequence in context: A129382 A163515 A220348 * A213711 A072649 A266082
Adjacent sequences: A274007 A274008 A274009 * A274011 A274012 A274013


KEYWORD

nonn


AUTHOR

Robert Israel, Jun 06 2016


STATUS

approved



