A055004 -id:A055004 - cp's OEIS frontend

A063483 S[A002808(n)] where S[] is Boris Stechkin's function (A055004) and A002808(n) are the composites.

0, 0, 15, 64, 171, 252, 359, 656, 1079, 1346, 1656, 2415, 3373, 3927, 4550, 5993, 6793, 7690, 8653, 9697, 12028, 14695, 16158, 17731, 19398, 21174, 25017, 27108, 29318, 34077, 39324, 42128, 45071, 51398, 54716, 58239, 61877, 65685, 73758

Offset: 0

Jason Earls, Jul 28 2001

nonn

Harry J. Smith, Table of n, a(n) for n=0,...,1000

Cf. A002808, A055004.

S(n)=sum(k=2,n,(k-1)*floor(n*(k-1)/k)); j=[]; for(n=0,80, if(isprime(n), n+1,j=concat(j,S(n)))); j

{ n=-1; for (m=0, 10^9, if (!isprime(m), a=sum(k=2, m, (k - 1)*floor(m*(k - 1)/k)); write("b063483.txt", n++, " ", a); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 23 2009

A062827 Variation of Stechkin's function, A055004.

Original entry on oeis.org

0, 4, 15, 45, 116, 259, 505, 853, 1378, 2256, 3249, 4855, 6730, 8738, 11348, 15012, 19533, 23693, 29693, 35876, 41890, 50691, 59467, 70667, 84999, 97916, 110050, 124679, 138413, 155289, 187442, 209595, 236182, 258438, 296293, 322458, 358076, 396409, 432326

Offset: 1

Jason Earls, Jul 20 2001

Cf. A055004.

for(n=1,22,print(sum(m=1,n,(prime(m-1)*floor(prime(n)*(prime(m-1)/ prime(m)))))))

More terms from Sean A. Irvine, Apr 09 2023

A274010 Boris Stechkin function: a(n) is the number of m with 2 <= m <= n and floor(n(m-1)/m) divisible by m-1.

Original entry on oeis.org

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

Offset: 0

Robert Israel, Jun 06 2016

nonn

Stechkin proves:
n-1 is prime iff a(n) = A000005(n).
n-1 and n+1 are twin primes, i.e., n is in A014574, iff a(n)+a(n+1) = 2*A000005(n).
If p < q are odd primes, then Sum_{k=p+1..q} (-1)^k a(k) = 0.

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

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

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

Cf. A000005, A014574, A055004.

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);

a[n_] := Sum[Boole[Divisible[Floor[n(m-1)/m], m-1]], {m, 2, n}];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 29 2019 *)

a(n)=sum(m=2,n,n*(m-1)\m%(m-1)==0) \\ Charles R Greathouse IV, Jun 08 2016

Conjecture: a(n) = tau(n) + tau(n-1) - 2, for n>=2. - Ridouane Oudra, Feb 28 2020

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A063483 S[A002808(n)] where S[] is Boris Stechkin's function (A055004) and A002808(n) are the composites.

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A062827 Variation of Stechkin's function, A055004.

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A274010 Boris Stechkin function: a(n) is the number of m with 2 <= m <= n and floor(n(m-1)/m) divisible by m-1.

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