A365422 Numbers k for which k and A163511(k) have the same prime signature.

3, 6, 7, 12, 14, 24, 28, 31, 45, 48, 55, 56, 62, 90, 96, 110, 111, 112, 119, 123, 124, 127, 175, 180, 192, 207, 220, 222, 224, 238, 246, 247, 248, 253, 254, 350, 360, 384, 414, 440, 444, 447, 448, 476, 492, 494, 496, 506, 508, 567, 700, 720, 768, 828, 880, 888, 894, 895, 896, 927, 945, 952, 957, 959, 984, 987, 988, 992

Offset: 1

Author

Antti Karttunen, Sep 04 2023

Keywords

• nonn

Comments

If k is present, then 2*k is also a term, and vice versa.

Crossrefs

Cf. A046523, A163511, A278531, A365421 (characteristic function).

Subsequences: A007283, A335431, A365423 (odd terms).

Programs

PARI

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365421(n) = (A046523(A163511(n))==A046523(n));
isA365422(n) = A365421(n);