# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a369169 Showing 1-1 of 1 %I A369169 #14 Jan 15 2024 10:03:21 %S A369169 1,16,1296,23040,810000,7257600,16934400,283852800,1437004800, %T A369169 1944810000,13970880000,30735936000,232475443200,852409958400, %U A369169 1765360396800,3269185920000,7192209024000,8029628006400,28473963210000,97893956160000,181803061440000,1086822696960000 %N A369169 Terms k of A025487 such that A000005(k) = A000688(k). %C A369169 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. %C A369169 From _David A. Corneth_, Jan 15 2024: (Start) %C A369169 16 | a(n) for n > 1. %C A369169 This sequence contains A002110(n)^4. (End) %D A369169 József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter II, page 73. %H A369169 Amiram Eldar, Table of n, a(n) for n = 1..377 %H A369169 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. %e A369169 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). %t A369169 lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; Select[lps, DivisorSigma[0, #] == FiniteAbelianGroupCount[#] &] %Y A369169 Cf. A000005, A000688, A002110, A046523, A124832. %Y A369169 Intersection of A025487 and A369168. %K A369169 nonn %O A369169 1,2 %A A369169 _Amiram Eldar_, Jan 15 2024 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE