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.

288, 1225, 4116, 35378, 54450, 1693776, 5969418, 9396618, 24509696310, 246465324525, 5876919827760, 71516027973936, 89547553939440, 370544528449590, 4014732589250736, 565869696542012100

Offset

1,1

Comments

If p is the largest prime divisor of a term k, then p^2 divides k. - Max Alekseyev, Feb 03 2024

Links

Table of n, a(n) for n=1..16.

Example

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.

Maple

with(numtheory): P:=proc(q) local a, k, n; for n from 1 to q do a:=ifactors(n)[2];
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);
fi; od; end: P(10^9);

Crossrefs

Subsequence of A073539.

Cf. A000010, A001414, A007947.

Sequence in context: A179646 A281236 A237369 * A250871 A128392 A296784

Adjacent sequences: A280933 A280934 A280935 * A280937 A280938 A280939

Keyword

nonn

Author

Paolo P. Lava, Jan 11 2017

Extensions

a(9)-a(16) from Max Alekseyev, Feb 03 2024

Status

approved