cp's OEIS Frontend

A280936 Numbers k such that phi(k) = rad(k) * sopfr(k), where phi(k) is the Euler totient function of k, rad(k) the squarefree kernel of k and sopfr(k) the integer log of k.

%I A280936 #14 Aug 27 2024 14:34:00
%S A280936 288,1225,4116,35378,54450,1693776,5969418,9396618,24509696310,
%T A280936 246465324525,5876919827760,71516027973936,89547553939440,
%U A280936 370544528449590,4014732589250736,565869696542012100
%N A280936 Numbers k such that phi(k) = rad(k) * sopfr(k), where phi(k) is the Euler totient function of k, rad(k) the squarefree kernel of k and sopfr(k) the integer log of k.
%C A280936 If p is the largest prime divisor of a term k, then p^2 divides k. - _Max Alekseyev_, Feb 03 2024
%e A280936 Prime factors of 288 are 2, 2, 2, 2, 2, 3, 3. Then phi(288) = 96, rad(288) = 2 * 3 = 6, sopfr(288) = 2 + 2 + 2 + 2 + 2 + 3 + 3 = 16 and 6 * 16 = 96.
%p A280936 with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=ifactors(n)[2];
%p A280936 if phi(n)=mul(a[k][1],k=1..nops(a))*add(a[k][1]*a[k][2],k=1..nops(a)) then print(n);
%p A280936 fi; od; end: P(10^9);
%Y A280936 Subsequence of A073539.
%Y A280936 Cf. A000010, A001414, A007947.
%K A280936 nonn
%O A280936 1,1
%A A280936 _Paolo P. Lava_, Jan 11 2017
%E A280936 a(9)-a(16) from _Max Alekseyev_, Feb 03 2024