A196220 Integer quotients of k^2 by the sum of the prime distinct divisors of k^2+1, where k = A196219(n).

7, 18, 121, 2268, 13520, 1377, 8550, 5157, 7381, 8496, 76176, 83521, 161604, 284229, 1028196, 4092529, 275804, 274432, 336985, 1153476, 962948, 48841, 319225, 276676, 617796, 3946827, 684450, 156349, 632025, 1256454, 6368547, 244917, 2506180, 2256004, 5410947

Offset

1,1

Comments

Generated by k = 7, 18, 187, 378, 1560, 1683, … (A196219).

Links

Amiram Eldar, Table of n, a(n) for n = 1..500 (calculated from the b-file at A196219)

Formula

a(n) = A196219(n)^2/A008472(A196219(n)^2 + 1). - Amiram Eldar, Mar 09 2020

Example

For k = 378, the prime distinct divisors of 378^2 + 1 are 5, 17, 41 and 378^2 /(5+17+41) = 2268. Hence 2268 is in the sequence.

Maple

with(numtheory):for k from 1 to 120000 do: y:=factorset(k^2+1): s:=sum(y[i], i=1..nops(y)):if irem(k^2, s)=0 then printf(`%d, `, k^2/s):else fi:od:

Mathematica

Select[Table[n^2/Total[Transpose[FactorInteger[n^2+1]][[1]]], {n, 10^5}], IntegerQ] (* Harvey P. Dale, Apr 18 2015 *)

Crossrefs

Cf. A002522, A008472, A180278, A196219.

Sequence in context: A207153 A203222 A197940 * A198031 A203118 A197656

Adjacent sequences: A196217 A196218 A196219 * A196221 A196222 A196223

Keyword

nonn

Author

Michel Lagneau, Sep 29 2011

Status

approved