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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).
2
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Feb 23 2019
STATUS
approved