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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.)