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

Author

Michel Marcus, Feb 23 2019

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000010, A000203, A006881.

Cf. A324331, A324333, A324334.

Programs

PARI

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