A051838 Numbers k such that sum of first k primes divides product of first k primes.
1, 3, 8, 13, 23, 38, 39, 41, 43, 48, 50, 53, 56, 57, 58, 66, 68, 70, 73, 77, 84, 90, 94, 98, 126, 128, 134, 140, 143, 145, 149, 151, 153, 157, 160, 164, 167, 168, 172, 174, 176, 182, 191, 194, 196, 200, 210, 212, 215, 217, 218, 219, 222, 225, 228, 229
Offset: 1
Keywords
Examples
Sum of first 8 primes is 77 and product of first 8 primes is 9699690. 77 divides 9699690 therefore a(3)=8.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Crossrefs
Programs
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GAP
P:=Filtered([1..2000],IsPrime);; Filtered([1..Length(P)],n->Product([1..n],i->P[i]) mod Sum([1..n],i->P[i])=0); # Muniru A Asiru, Dec 20 2018
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Haskell
import Data.List (elemIndices) a051838 n = a051838_list !! (n-1) a051838_list = map (+ 1) $ elemIndices 0 $ zipWith mod a002110_list a007504_list -- Reinhard Zumkeller, Oct 03 2011
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Mathematica
p = Prime@ Range@ 250; Flatten@ Position[ Mod[ First@#, Last@#] & /@ Partition[ Riffle[ Rest[ FoldList[ Times, 1, p]], Accumulate@ p], 2], 0] (* Harvey P. Dale, Dec 19 2010 *)
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PARI
for(n=1,100,P=prod(i=1,n,prime(i));S=sum(i=1,n,prime(i));if(!(P%S),print1(n,", "))) \\ Derek Orr, Jul 19 2015
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PARI
isok(n) = my(p = primes(n)); (vecprod(p) % vecsum(p)) == 0; \\ Michel Marcus, Dec 20 2018