This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090882 #11 Apr 28 2022 07:59:10
%S A090882 0,1,5,2,25,6,125,3,10,26,625,7,3125,126,30,4,15625,11,78125,27,130,
%T A090882 626,390625,8,50,3126,15,127,1953125,31,9765625,5,630,15626,150,12,
%U A090882 48828125,78126,3130,28,244140625,131,1220703125,627,35,390626,6103515625,9,250
%N A090882 Suppose n=(p1^e1)(p2^e2)... where p1,p2,... are the prime numbers and e1,e2,... are nonnegative integers. Then a(n) = e1 + (e2)*5 + (e3)*25 + (e4)*125 + ... + (ek)*(5^(k-1)) + ...
%C A090882 Replace "5" with "x" and extend the definition of a to positive rationals and a becomes an isomorphism between positive rationals under multiplication and polynomials over Z under addition. This remark generalizes A001222, A048675 and A054841: evaluate said polynomial at x=1, x=2 and x=10, respectively.
%D A090882 Joseph J. Rotman, The Theory of Groups: An Introduction, 2nd ed. Boston: Allyn and Bacon, Inc. 1973. Page 9, problem 1.26.
%H A090882 Antti Karttunen, <a href="/A090882/b090882.txt">Table of n, a(n) for n = 1..1001</a>
%H A090882 Sam Alexander, <a href="http://tinyurl.com/yzjw">Post to sci.math</a>.
%o A090882 (PARI) A090882(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*5^(primepi(f[k, 1])-1)); }; \\ _Antti Karttunen_, Apr 28 2022
%Y A090882 Cf. A001222, A048675, A054841, A090880, A090881, A090883, A090884, and also A195017, A248663, A276075, A276085.
%K A090882 easy,nonn
%O A090882 1,3
%A A090882 _Sam Alexander_, Dec 12 2003
%E A090882 More terms from _Ray Chandler_, Dec 20 2003