A324332 Numbers m such that A324331(m) = (m-1)^2 - phi(m)*sigma(m) is a square, even though they are not squarefree semiprimes (A006881).

12, 20, 24, 40, 42, 44, 45, 48, 63, 72, 80, 96, 104, 105, 108, 132, 135, 160, 189, 190, 192, 200, 216, 275, 320, 342, 384, 385, 399, 405, 429, 452, 456, 465, 567, 575, 610, 637, 639, 640, 648, 693, 768, 783, 848, 969, 988, 1000, 1015, 1044, 1098, 1105, 1127, 1210, 1215

Offset

1,1

Comments

If m is a squarefree semiprime, then A324331(m) is a square. But the converse is not always true.

Links

Table of n, a(n) for n=1..55.

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

Example

A324331(45) = 64, a square, even though 45 is not squarefree semiprime, so 45 is a term.

Prog

(PARI) f(n) = (n-1)^2 - eulerphi(n)*sigma(n); \\ A324331
isok(n) = !((bigomega(n) == 2) && issquarefree(n)) && issquare(f(n));

Crossrefs

Cf. A000010, A000203, A006881.

Cf. A324331, A324333, A324334.

Sequence in context: A286004 A055598 A302297 * A035511 A095035 A108027

Adjacent sequences: A324329 A324330 A324331 * A324333 A324334 A324335

Keyword

nonn

Author

Michel Marcus, Feb 23 2019

Status

approved