A226448 Composite squarefree numbers k such that the ratios (k - 1/2)/(p - 1/2) are integers for each prime p dividing k.

260054438, 597892523, 1200695738, 3287998643, 3423456563, 10524308498, 13292859563, 15646705718, 19441707170, 33309521438, 38848586123, 43312628678, 61899936935, 72422400713, 75439031063, 85338414662, 112419230963, 132624705038, 136084511063, 141236121758

Offset

1,1

Comments

Also composite squarefree numbers k such that (2p - 1) | (2k - 1).

Links

Giovanni Resta, Table of n, a(n) for n = 1..45 (terms < 10^12)

Example

3287998643 is a term since it is equal to 743*787*5623 and 3287998643-1/2 divided by 743-1/2, 787-1/2 and 5623-1/2 gives 3 integers, namely 4428281, 4180545 and 584793.

Maple

with(numtheory); ListA226448:=proc(i, j) local c, d, n, ok, p;
for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
for d from 1 to nops(p) do if p[d][2]>1 or not type((n-j)/(p[d][1]-j), integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: ListA226448(10^9, 1/2); # Paolo P. Lava, Oct 06 2013

Prog

(PARI) is(n, P)=n=2*n-1; for(i=1, #P, if(n%(2*P[i]-1), return(0))); 1
list(lim, P=[], n=1, mx=lim\2)=my(v=[], t); if(#P>1&&is(n, P), v=[n]); P=concat(P, 0); forprime(p=2, min(lim, mx), P[#P]=p; t=list(lim\p, P, n*p, p-1); if(#t, v=concat(v, t))); v \\ Charles R Greathouse IV, Jun 07 2013

Crossrefs

Cf. A208728, A225702-A225720, A226020, A226111-A226114, A226364.

Sequence in context: A205934 A375975 A231202 * A250433 A329464 A332314

Adjacent sequences: A226445 A226446 A226447 * A226449 A226450 A226451

Keyword

nonn

Author

Paolo P. Lava and Giovanni Resta, Jun 07 2013

Status

approved