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 A263546 Numbers k such that k divides the sum of the first k primes with even indices. 1
 1, 2, 6, 12, 15, 28, 40, 92, 111, 113, 145, 223, 268, 420, 625, 2080, 2282, 2996, 3371, 19560, 38032, 54426, 1474778, 3763906, 5196340, 6435993, 7808592, 11487666, 16738298, 28145334, 53830258, 57281504, 77275294, 135770496, 164914949 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS There are 15 values of a(n) < 1000 although A045345 has 4 values A045345(n) < 1000. How do these sequences compare asymptotically? LINKS EXAMPLE 1 is in the sequence because prime(2) = 3 is divisible by 1. 2 is in the sequence because prime(2) + prime(4) = 3 + 7 = 10 is divisible by 2. MATHEMATICA Select[Range@ 10000, Divisible[Sum[Prime[2 i], {i, 1, #}], #] &] (* Michael De Vlieger, Oct 21 2015 *) PROG (PARI) list(lim)=my(v=List(), k, s, t); forprime(p=2, , if((t++) && t%2==0, s+=p; k++; if(s%k==0, listput(v, k)); if(k>=lim, return(Vec(v))))) CROSSREFS Cf. A031215, A045345, A077126, A263541. Sequence in context: A285312 A065154 A230482 * A143408 A191331 A088915 Adjacent sequences:  A263543 A263544 A263545 * A263547 A263548 A263549 KEYWORD nonn AUTHOR Altug Alkan, Oct 20 2015 STATUS approved

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Last modified January 27 12:56 EST 2022. Contains 350607 sequences. (Running on oeis4.)