The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A225717 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A225717

Composite squarefree numbers n such that p(i)+7 divides n-7, where p(i) are the prime factors of n.
(history; published version)

#12 by T. D. Noe at Fri May 17 15:50:00 EDT 2013

STATUS

editing

approved

#11 by T. D. Noe at Fri May 17 15:49:56 EDT 2013

MATHEMATICA

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 7, p + 7]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

STATUS

approved

editing

#10 by T. D. Noe at Fri May 17 11:37:31 EDT 2013

STATUS

editing

approved

#9 by T. D. Noe at Fri May 17 11:37:25 EDT 2013

CROSSREFS

Cf. A208728, A225702-A225716, A225718-A225720.

#8 by T. D. Noe at Fri May 17 11:37:12 EDT 2013

NAME

Composite squarefree numbers n such that p(i)+7| divides n-7, where p(i) are the prime factors of n.

STATUS

proposed

editing

#7 by Paolo P. Lava at Fri May 17 02:31:29 EDT 2013

STATUS

editing

proposed

#6 by Paolo P. Lava at Fri May 17 02:31:23 EDT 2013

EXAMPLE

Prime factors of 15847 are 13, 23 and 53. We have that (13+7)|(15847-7)/(13+7) = 792, (23+7)|(15847-7)/(23+7) = 528 and (53+7)|(15847-7)/(53+7) = 264.

#5 by T. D. Noe at Thu May 16 13:14:51 EDT 2013

STATUS

proposed

editing

#4 by Paolo P. Lava at Thu May 16 05:27:05 EDT 2013

STATUS

editing

proposed

#3 by Paolo P. Lava at Wed May 15 09:01:52 EDT 2013

LINKS

Paolo P. Lava, <a href="/A225717/b225717.txt">Table of n, a(n) for n = 1..100</a>

MAPLE

for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;

if 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: A225717(10^9, -7);