A369169 Terms k of A025487 such that A000005(k) = A000688(k).

1, 16, 1296, 23040, 810000, 7257600, 16934400, 283852800, 1437004800, 1944810000, 13970880000, 30735936000, 232475443200, 852409958400, 1765360396800, 3269185920000, 7192209024000, 8029628006400, 28473963210000, 97893956160000, 181803061440000, 1086822696960000

Offset: 1

Author

Amiram Eldar, Jan 15 2024

Keywords

• nonn

Comments

Since both A000005(k) and A000688(k) depend only on the prime signature of k (A124832), if k is a term of this sequence then every number m such that A046523(m) = k is a term of A369168.

From David A. Corneth, Jan 15 2024: (Start)

16 | a(n) for n > 1.

This sequence contains A002110(n)^4. (End)

Examples

			16 is in the sequence as 16 has 5 divisors (1, 2, 4, 8, 16) and 5 factorizations into prime powers (16 = 2*8 = 4*4 = 2*2*4 = 2*2*2*2).
		

References

• József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter II, page 73.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..377
• Aleksandar Ivić, On the number of abelian groups of a given order and on certain related multiplicative functions, Journal of Number Theory, Vol. 16, No. 1 (1983), pp. 119-137.

Crossrefs

Cf. A000005, A000688, A002110, A046523, A124832.

Intersection of A025487 and A369168.

Programs

Mathematica

lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]; Select[lps, DivisorSigma[0, #] == FiniteAbelianGroupCount[#] &]