A351449 a(n) = A064989(A295294(A003961(n))).

1, 1, 1, 11, 1, 1, 1, 3, 29, 1, 1, 11, 1, 1, 1, 49, 1, 29, 1, 11, 1, 1, 1, 3, 34, 1, 22, 11, 1, 1, 1, 55, 1, 1, 1, 319, 1, 1, 1, 3, 1, 1, 1, 11, 29, 1, 1, 49, 85, 34, 1, 11, 1, 22, 1, 3, 1, 1, 1, 11, 1, 1, 29, 1091, 1, 1, 1, 11, 1, 1, 1, 87, 1, 1, 34, 11, 1, 1, 1, 49, 469, 1, 1, 11, 1, 1, 1, 3, 1

Offset: 1

Author

Antti Karttunen, Feb 11 2022

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A048250, A057521, A064989, A151800, A295294, A326042, A351450, A351451.

Programs

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]));
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521
A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A295294(n) = sigma(A057521(n));
A351449(n) = A064989(A295294(A003961(n)));

Formula

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

a(n) = A064989(A295294(A003961(n))) = A326042(A057521(n)).

a(n) = A326042(n) / A351451(n).