A351451 a(n) = A064989(A092261(A003961(n))).

1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 5, 2, 4, 2, 2, 1, 3, 1, 2, 1, 4, 5, 6, 2, 1, 4, 1, 2, 1, 2, 17, 1, 10, 3, 2, 1, 10, 2, 8, 1, 7, 4, 2, 5, 1, 6, 8, 2, 1, 1, 6, 4, 6, 1, 5, 2, 4, 1, 29, 2, 13, 17, 2, 1, 4, 10, 4, 3, 12, 2, 31, 1, 3, 10, 2, 2, 10, 8, 10, 1, 1, 7, 12, 4, 3, 2, 2, 5, 25, 1, 8, 6, 34, 8, 2

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Formula

Multiplicative with a(p) = A064989(q+1) and a(p^e) = 1 for e > 1, where q = nextPrime(p) = A151800(p).

a(n) = A351450(A055231(n)) = A064989(A092261(A003961(n))).

a(n) = A326042(n) / A351449(n).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A055231(n) = {my(f=factor(n)); for (k=1, #f~, if (f[k, 2] > 1, f[k, 2] = 0); ); factorback(f); } \\ From A055231
A064989(n) = { my(f = factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A351450(n) = A064989(A048250(A003961(n)));
A351451(n) = A351450(A055231(n));

Crossrefs

Cf. A003961, A048250, A055231, A064989, A092261, A151800, A351449, A351450.

Sequence in context: A273134 A126207 A276711 * A191322 A264840 A308188

Adjacent sequences: A351448 A351449 A351450 * A351452 A351453 A351454

Keyword

nonn,mult

Author

Antti Karttunen, Feb 11 2022

Status

approved