The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261530 Numbers k such that k^2 + 1 = p*q*r*s where p,q,r,s are distinct primes and the sum p+q+r+s is a perfect square. 0
 173, 187, 477, 565, 965, 1237, 1277, 1437, 1525, 1636, 2452, 2587, 2608, 2653, 2827, 2885, 2971, 3197, 3388, 3412, 3435, 3477, 3848, 3891, 4188, 4237, 4492, 4724, 5333, 5728, 5899, 6272, 7088, 7108, 7421, 8363, 8541, 9379, 9652, 10227, 10872, 11581, 12237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The primes in the sequence are 173, 1237, 1277, 2971, 5333, 8363, 19387, 20773, ... The corresponding squares p+q+r+s are 121, 289, 441, 289, 529, 9025, 841, 5625, 529, 196, 5476, 3025, ... LINKS Table of n, a(n) for n=1..43. EXAMPLE 173 is in the sequence because 173^2 + 1 = 2*5*41*73 and 2 + 5 + 41 + 73 = 11^2. MAPLE with(numtheory): for n from 1 to 20000 do: y:=factorset(n^2+1):n0:=nops(y): if n0=4 and bigomega(n^2+1)=4 and sqrt(y[1]+y[2]+y[3]+y[4])=floor(sqrt(y[1]+y[2]+y[3]+y[4])) then printf(`%d, `, n): else fi: od: PROG (PARI) isok(n) = my(f = factor(n^2+1)); (#f~== 4) && (vecmax(f[, 2]) == 1) && issquare(vecsum(f[, 1])) ; \\ Michel Marcus, Aug 24 2015 CROSSREFS Cf. A002522, A261529. Sequence in context: A259017 A097845 A364937 * A246135 A140002 A178652 Adjacent sequences: A261527 A261528 A261529 * A261531 A261532 A261533 KEYWORD nonn AUTHOR Michel Lagneau, Aug 24 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 08:45 EDT 2024. Contains 373424 sequences. (Running on oeis4.)