A072004 -id:A072004 - cp's OEIS frontend

A077023 Integer values of sum of first k primes squared divided by k-th prime, for some k (A077022).

2, 29, 284, 410066261, 941945317

Offset: 1

Randy L. Ekl, Zak Seidov, Oct 17 2002

Remainder, a(n), when sum of first n primes squared is divided by n-th prime in A072004. In A077023, 5 values of n such that a(n)=0 are given. In the sequence, the corresponding integer values of sum of first n primes squared divided by n-th prime are given. For primes <100,000,000, there are no other cases of a(n)=0.

			29 is a term because A024450(6)/prime(6) = 29;
284 is a term because A024450(17)/prime(17) = 284;
410066261 is a term because A024450(11156)/prime(11156) = 410066261;
941945317 is a term because A024450(16548)/prime(16548) = 941945317.

Cf. A024450, A072004, A077022.

a(n) = A024450(A077022(n))/prime(A077022(n)). - Michel Marcus, Jan 14 2023

A077022 Values of k such that sum of first k primes squared is divisible by k-th prime.

Original entry on oeis.org

1, 6, 17, 11156, 16548

Offset: 1

Randy L. Ekl and Zak Seidov, Oct 17 2002

Numbers k such that A072004(k) = 0.

a(6) > 10^11. - Giovanni Resta, Mar 07 2013

			6 is a term because A024450(6)/prime(6) = 29;
17 is a term because A024450(17)/prime(17) = 284;
11156 is a term because A024450(11156)/prime(11156) = 410066261;
16548 is a term because A024450(16548)/prime(16548) = 941945317.

Cf. A024450, A072004, A077023.

Module[{nn=17000,prs},prs=Accumulate[Prime[Range[nn]]^2];Select[Range[ nn],Divisible[prs[[#]],Prime[#]]&]] (* Harvey P. Dale, Nov 23 2013 *)

cp's OEIS Frontend

A077023 Integer values of sum of first k primes squared divided by k-th prime, for some k (A077022).

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