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A324331 a(n) = (n-1)^2 - phi(n)*sigma(n), where phi is A000010 and sigma is A000203. 3
-1, -2, -4, -5, -8, 1, -12, -11, -14, 9, -20, 9, -24, 25, 4, -23, -32, 55, -36, 25, 16, 81, -44, 49, -44, 121, -44, 57, -56, 265, -60, -47, 64, 225, 4, 133, -72, 289, 100, 81, -80, 529, -84, 169, 64, 441, -92, 225, -90, 541, 196, 249, -104, 649, 36, 145, 256, 729, -116, 793 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For squarefree semiprimes n = p*q  a(n)=(p-q)^2 is a square. But the converse, a(n) is prime, can happen: see A324332.

LINKS

Table of n, a(n) for n=1..60.

B. Alspach, Research problems, Problem 18, Discrete Math 40 (1982), page 126.

FORMULA

a(A006881(n)) = A176881(n)^2.

MATHEMATICA

Table[(n-1)^2 - EulerPhi[n]*DivisorSigma[1, n], {n, 1, 60}] (* Vaclav Kotesovec, Feb 23 2019 *)

PROG

(PARI) a(n) = (n-1)^2 - eulerphi(n)*sigma(n);

CROSSREFS

Cf. A000010, A000203, A006881, A176881.

Cf. A324332, A324333, A324334.

Sequence in context: A301521 A097698 A233524 * A101410 A110991 A262942

Adjacent sequences:  A324328 A324329 A324330 * A324332 A324333 A324334

KEYWORD

sign

AUTHOR

Michel Marcus, Feb 23 2019

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)