A339893 -id:A339893 - cp's OEIS frontend

A339895 a(n) = A339894(n) - A061395(n).

0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 2, 2, 1, 1, 0, 3, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 1, 1, 0, 1, 1, 2, 0, 3, 0, 0, 3, 1, 2, 1, 0, 2, 3, 0, 0, 2, 1, 0, 1, 1, 0, 3, 2, 1, 1, 0, 1, 2, 0, 3, 2, 2, 0, 1, 0, 1, 3

Offset: 1

Antti Karttunen, Dec 21 2020

nonn

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

Cf. A000523, A061395, A122111, A334201, A339893, A339894, A339896.

Cf. A339897 (first occurrence of each n).

A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A339894(n) = A000523(A122111(n));
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A339895(n) = (A339894(n)-A061395(n));

a(n) = A339894(n) - A061395(n).
a(n) = A334201(n) - A339896(n).
a(n) = A339893(A122111(n)).

A342657 The difference between floor(log_2(.)) of and the number of prime factors in A156552(n) (when counted with multiplicity).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 1, 1, 0, 2, 0, 3, 1, 3, 0, 3, 0, 4, 1, 3, 0, 2, 0, 3, 3, 5, 1, 1, 0, 7, 3, 3, 0, 4, 0, 5, 2, 5, 0, 4, 0, 2, 4, 6, 0, 3, 1, 5, 5, 7, 0, 4, 0, 9, 3, 2, 3, 4, 0, 6, 7, 4, 0, 3, 0, 10, 2, 7, 1, 5, 0, 5, 1, 11, 0, 3, 3, 11, 5, 3, 0, 2, 1, 8, 7, 11, 4, 4, 0, 3, 3, 3, 0, 5, 0, 7, 2

Offset: 2

Antti Karttunen, Mar 18 2021

nonn

Cf. A000430 (positions of 0's), A000523, A001222, A003961, A061395, A070939, A156552, A246277, A322993, A325134, A339893, A342655, A342656.

Cf. also A339895.

A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
A342657(n) = { my(u=A156552(n)); (#binary(u)-bigomega(u))-1; };

a(n) = A339893(A156552(n)) = A339893(A322993(n)) = A000523(A156552(n)) - A001222(A156552(n)).
a(n) = (A252464(n)-A342655(n))-1 = (A325134(n)-A342655(n)) - 2.
a(p) = a(p^2) = 0 for all primes p. (Second part added Jul 27 2023)
a(A003961(n)) = a(2*A246277(n)) = a(n).

cp's OEIS Frontend

A339895 a(n) = A339894(n) - A061395(n).

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