A296078 Least number with the same prime signature as 1+phi(n), where phi = A000010, Euler totient function.

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 4, 2, 2, 2, 4, 6, 2, 2, 2, 2, 4, 2, 2, 6, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 6, 4, 2, 2, 2, 2, 6, 6, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 6, 4, 6, 2, 6, 12, 4, 2, 4, 2, 2, 2, 2, 2, 4, 2, 6, 6, 2, 2, 4, 6, 2, 6, 2, 2, 4, 2, 12, 2, 2, 2, 6, 2, 2, 2, 2, 2, 6, 2, 4, 4

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A046523(A039649(n)) = A046523(1+A000010(n)).

Mathematica

f[n_] := Block[{ps = Last@# & /@ FactorInteger[1 + EulerPhi@n]}, Times @@ ((Prime@ Range@ Length@ ps)^ps)]; Array[f, 105] (* Robert G. Wilson v, Dec 11 2017 *)

Prog

(PARI)
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from Charles R Greathouse IV, Aug 17 2011
A296078(n) = A046523(1+eulerphi(n));

Crossrefs

Cf. A000010, A046523, A039649, A296079, A296080.

Cf. A039698 (positions of 2's).

Cf. also A277906, A296076, A296085, A296092.

Sequence in context: A236362 A133502 A341422 * A137325 A180258 A211663

Adjacent sequences: A296075 A296076 A296077 * A296079 A296080 A296081

Keyword

nonn

Author

Antti Karttunen, Dec 05 2017

Status

approved