A354202 Fully multiplicative with a(p^e) = A354200(A000720(p))^e.

1, 5, 7, 25, 13, 35, 11, 125, 49, 65, 19, 175, 17, 55, 91, 625, 29, 245, 23, 325, 77, 95, 31, 875, 169, 85, 343, 275, 37, 455, 43, 3125, 133, 145, 143, 1225, 41, 115, 119, 1625, 53, 385, 47, 475, 637, 155, 59, 4375, 121, 845, 203, 425, 61, 1715, 247, 1375, 161, 185, 67, 2275, 73, 215, 539, 15625, 221, 665, 71, 725

Offset: 1

Author

Antti Karttunen, May 23 2022

Keywords

• nonn
• mult

Comments

Permutation of A007310. Preserves the prime signature.

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A007310 (terms sorted into ascending order), A354200, A354203 (left inverse), A354204 (Möbius transform), A354205 (inverse Möbius transform).

Cf. also A003961, A108548, A267099, A332818, A348746, A354091 for similar constructions.

Programs

PARI

A354200(n) = if(1==n,5,my(p=prime(n), m=p%4); forprime(q=1+p,,if(m==(q%4),return(q))));
A354202(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354200(primepi(f[k,1]))); factorback(f); };