The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A077022 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A077022

Values of k such that sum of first k primes squared is divisible by k-th prime.
(history; published version)

#22 by Michael De Vlieger at Sat Jan 14 08:44:39 EST 2023

STATUS

reviewed

approved

#21 by Joerg Arndt at Sat Jan 14 07:09:36 EST 2023

STATUS

proposed

reviewed

#20 by Michel Marcus at Sat Jan 14 05:56:59 EST 2023

STATUS

editing

proposed

#19 by Michel Marcus at Sat Jan 14 05:56:56 EST 2023

CROSSREFS

Cf. A024450, A072004, A077023.

#18 by Michel Marcus at Sat Jan 14 05:56:27 EST 2023

COMMENTS

Numbers k such that A072004(k) = 0.

EXAMPLE

6 is OK because (p(1)^2+...+p(6)^2)/p(6)=29; 17 is OK because (p(1)^2+...+p(17)^2)/p(17)=284; 11156 is OK because (p(1)^2+...+p(11156)^2)/p(11156)=410066261; 16548 is OK because (p(1)^2+...+p(16548 )^2)/p(16548)=941945317.

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.

#17 by Michel Marcus at Sat Jan 14 05:53:26 EST 2023

NAME

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

COMMENTS

Remainder, a(n), when sum of first n primes squared is divided by n-th prime in A072004. In A072004, in three cases, a(n)=0 that is the sum of squares of first n primes is divisible by n-th prime. Here we added two more cases when a(n)=0.

#16 by Michel Marcus at Sat Jan 14 05:50:08 EST 2023

KEYWORD

nonn,more

STATUS

approved

editing

#15 by Charles R Greathouse IV at Thu Mar 19 09:38:16 EDT 2015

AUTHOR

_Randy L. Ekl (Randy.Ekl(AT)Motorola.com) _ and Zak Seidov, Oct 17 2002

Discussion

Thu Mar 19

09:38

OEIS Server: https://oeis.org/edit/global/2378

#14 by Harvey P. Dale at Sat Nov 23 11:31:38 EST 2013

STATUS

editing

approved

#13 by Harvey P. Dale at Sat Nov 23 11:31:32 EST 2013

MATHEMATICA

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

STATUS

approved

editing