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A289320 a(n) = A289310(n)^2 + A289311(n)^2. 3
1, 5, 10, 25, 26, 50, 50, 125, 100, 130, 122, 250, 170, 250, 260, 625, 290, 500, 362, 650, 500, 610, 530, 1250, 676, 850, 1000, 1250, 842, 1300, 962, 3125, 1220, 1450, 1300, 2500, 1370, 1810, 1700, 3250, 1682, 2500, 1850, 3050, 2600, 2650, 2210, 6250, 2500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is totally multiplicative.

a(n) > n^2 for any n > 1.

If n is a square, then a(n) is a square.

If a(n) and a(m) are squares, then a(n*m) is a square.

a(n) is also a square for nonsquares n = 42, 168, 246, 287, 378, 672, 984, 1050, 1148, 1434, 1512, 1673, 2058, 2214, 2583, 2688, ...

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

FORMULA

Totally multiplicative, with a(p^k) = (1 + p^2)^k for any prime p and k > 0.

PROG

(PARI) a(n) = my (f=factor(n)); return (prod(i=1, #f~, (1 + f[i, 1]^2) ^ f[i, 2]))

(Python)

from sympy import factorint

from operator import mul

def a(n): return 1 if n==1 else reduce(mul, [(1 + p**2)**k for p, k in factorint(n).items()])

print map(a, range(1, 101)) # Indranil Ghosh, Aug 03 2017

CROSSREFS

Cf. A066872, A289310, A289311.

Sequence in context: A177432 A269740 A166635 * A078308 A083493 A061259

Adjacent sequences:  A289317 A289318 A289319 * A289321 A289322 A289323

KEYWORD

nonn,mult

AUTHOR

Rémy Sigrist, Jul 02 2017

STATUS

approved

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Last modified January 26 17:31 EST 2020. Contains 331280 sequences. (Running on oeis4.)