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

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