A331312 a(n) = A225546(n) / A293442(n).

1, 1, 2, 1, 8, 2, 128, 1, 3, 8, 32768, 2, 2147483648, 128, 16, 1, 9223372036854775808, 3, 170141183460469231731687303715884105728, 8, 256, 32768, 57896044618658097711785492504343953926634992332820282019728792003956564819968, 2, 27, 2147483648, 6, 128

Offset: 1

Author

Antti Karttunen, Jan 21 2020

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A000225, A019565, A225546, A293442, A331311.

Programs

PARI

A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A331312(n) = { my(f=factor(n)); for (i=1, #f~, my(p=f[i, 1]); f[i, 1] = A019565(f[i, 2]); f[i, 2] = (2^(primepi(p)-1))-1; ); factorback(f); };

Formula

a(n) = A225546(n) / A293442(n).

Multiplicative, with a(prime(i)^j) = A019565(j)^A000225(i-1).