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

1,2

Comments

Permutation of A007310. Preserves the prime signature.

Links

Table of n, a(n) for n=1..68.

Index entries for sequences computed from indices in prime factorization

Prog

(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); };

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.

Sequence in context: A298900 A357852 A166660 * A037374 A056717 A072370

Adjacent sequences: A354199 A354200 A354201 * A354203 A354204 A354205

Keyword

nonn,mult

Author

Antti Karttunen, May 23 2022

Status

approved