A339893 -id:A339893

The OEIS is supported by the many generous donors to the OEIS Foundation.

Search: a339893 -id:a339893

Displaying 1-2 of 2 results found.

page 1

A339895

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

+10
7

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,27

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

FORMULA

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

a(n) = A334201(n) - A339896(n).

a(n) = A339893(A122111(n)).

PROG

(PARI)

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));

CROSSREFS

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

Cf. A339897 (first occurrence of each n).

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 21 2020

STATUS

approved

A342657

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

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,11

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..10000 (based on Hans Havermann's factorization of A156552)

Index entries for sequences computed from indices in prime factorization

FORMULA

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).

PROG

(PARI)

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; };

CROSSREFS

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

Cf. also A339895.