A211176 - OEIS

A211176

Numbers n which are the hypotenuse of a Pythagorean triple with n' as a leg, where n' is the arithmetic derivative of n.

125, 625, 23125, 142805, 210125, 371293, 7983625, 9370805, 25757525, 50062025, 120670225, 489766225, 881052625, 1471596725, 2307267625, 2489771125, 3145529225, 3474871553, 6975757441, 7977558641

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

This sequence is a subsequence of A008846. - Ray Chandler, Jan 27 2017

LINKS

Table of n, a(n) for n=1..20.

FORMULA

A002144(n)^A002365(n) and A002144(n)^A002366(n) are terms of the sequence for all n. - Ray Chandler, Jan 27 2017

EXAMPLE

n = 23125, n' = 19125 and sqrt(n^2-n'^2) = 13000.

MAPLE

with(numtheory); ListA211176:= proc(q)local a, n, p;

for n from 2 to q do a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);

if n<>a and type(sqrt(n^2-a^2), integer) then print(n); fi;

od; end: ListA211176(10^9);

CROSSREFS

Cf. A002144, A002365, A002366, A003415, A008846, A009003, A009004, A210503.

Sequence in context: A034290 A295025 A070308 * A045170 A235896 A250634

Adjacent sequences: A211173 A211174 A211175 * A211177 A211178 A211179

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Feb 01 2013

EXTENSIONS

Name and Maple program corrected by Paolo P. Lava, Sep 30 2013

a(12)-a(16) from Donovan Johnson, Sep 30 2013

a(17)-a(18) from Ray Chandler, Jan 25 2017

a(19)-a(20) from Ray Chandler, Jan 27 2017

STATUS

approved