Revision History for A105210
(Underlined text is an addition;
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Showing entries 1-10
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#20 by Harvey P. Dale at Sat Mar 02 11:08:30 EST 2019
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#19 by Harvey P. Dale at Sat Mar 02 11:08:25 EST 2019
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| NAME
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a(1) = 393; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).). edit
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| MATHEMATICA
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nxt[n_]:=n+1+Total[Select[FactorInteger[n][[All, 1]], #<n&]]; NestList[ nxt, 393, 50] (* Harvey P. Dale, Mar 02 2019 *)
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approved
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#18 by Joerg Arndt at Fri Aug 18 03:17:13 EDT 2017
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#17 by Michel Marcus at Fri Aug 18 00:31:05 EDT 2017
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#16 by Michel Marcus at Fri Aug 18 00:31:01 EDT 2017
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| REFERENCES
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Problem 886, Math. Mag., 48 (1975), 57-58.
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| LINKS
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Doug Engel, <a href="http://www.jstor.org/stable/2689298">Problem 886</a>, Math. Mag., 48 (1975), 57-58.
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| STATUS
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proposed
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#15 by Jon E. Schoenfield at Thu Aug 17 23:21:04 EDT 2017
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#14 by Jon E. Schoenfield at Thu Aug 17 23:21:02 EDT 2017
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| NAME
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a(1) = 393; for n> > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
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| LINKS
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T. D. Noe, <a href="/A105210/b105210.txt">Table of n, a(n) for n= = 1..2000</a>
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| MAPLE
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with(numtheory): p:=proc(n) local nn, ct, s: if isprime(n)=true then s:=0 else nn:=convert(factorset(n), list): ct:=nops(nn): s:=sum(nn[j], j=1..ct):fi: end: a[1]:=393: for n from 2 to 50 do a[n]:=1+a[n-1]+p(a[n-1]) od:seq(a[n], n=1..50); # _Emeric Deutsch__, Apr 14 2005
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| CROSSREFS
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Cf. A027748, A003508, A027748, A105211, A105212, A105213.
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approved
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#13 by Jon E. Schoenfield at Thu Jul 30 23:14:48 EDT 2015
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#12 by Jon E. Schoenfield at Thu Jul 30 23:14:40 EDT 2015
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| EXAMPLE
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a(2)=528 because a(1)=393, the distinct prime factors of a(1) are 3 and 131; finally, 1+ + 393+ + 3+ + 131= = 528.
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| MAPLE
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with(numtheory): p:=proc(n) local nn, ct, s: if isprime(n)=true then s:=0 else nn:=convert(factorset(n), list): ct:=nops(nn): s:=sum(nn[j], j=1..ct):fi: end: a[1]:=393: for n from 2 to 50 do a[n]:=1+a[n-1]+p(a[n-1]) od:seq(a[n], n=1..50); (); # _Emeric Deutsch)_
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| MATHEMATICA
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a[1] = 393; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 44}] (from _}] (* _Robert G. Wilson v_, Apr 14 2005) *)
a[1] = 412; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 43}] (from _}] (* _Robert G. Wilson v_, Apr 14 2005) *)
a[1] = 668; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (from _}] (* _Robert G. Wilson v_, Apr 14 2005) *)
a[1] = 932; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (from _}] (* _Robert G. Wilson v_, Apr 14 2005) *)
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| AUTHOR
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R. K. Guy, Apr 14, 2005
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| STATUS
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approved
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#11 by Reinhard Zumkeller at Thu Jan 15 14:34:08 EST 2015
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