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A320111 Number of divisors d of n that are not of the form 4k+2. 10
1, 1, 2, 2, 2, 2, 2, 3, 3, 2, 2, 4, 2, 2, 4, 4, 2, 3, 2, 4, 4, 2, 2, 6, 3, 2, 4, 4, 2, 4, 2, 5, 4, 2, 4, 6, 2, 2, 4, 6, 2, 4, 2, 4, 6, 2, 2, 8, 3, 3, 4, 4, 2, 4, 4, 6, 4, 2, 2, 8, 2, 2, 6, 6, 4, 4, 2, 4, 4, 4, 2, 9, 2, 2, 6, 4, 4, 4, 2, 8, 5, 2, 2, 8, 4, 2, 4, 6, 2, 6, 4, 4, 4, 2, 4, 10, 2, 3, 6, 6, 2, 4, 2, 6, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Inverse Möbius transform of A152822.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20160

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

FORMULA

a(n) = Sum_{d|n, d == 0, 1 or 3 mod 4} 1.

Multiplicative with a(2^e) = e, a(p^e) = (e+1) for odd primes p.

a(2n) = A000005(n), a(2n+1) = A000005(2n+1).

a(n) = A000005(A252463(n)).

a(1) = a(2) = 1; for n > 2, a(n) = A001511(A252463(n)) * a(A000265(A252463(n))).

PROG

(PARI) A320111(n) = sumdiv(n, d, (2!=(d%4)));

(PARI) A320111(n) = {my(f); f = factor(n); for(i=1, #f~, if(f[i, 1]>2, f[i, 2]++)); factorback(f[, 2])};

(PARI)

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A252463(n) = if(!(n%2), n/2, A064989(n));

A320111(n) = numdiv(A252463(n));

(PARI)

\\ A252463 given above

A001511(n) = 1+valuation(n, 2);

A000265(n) = (n>>valuation(n, 2));

A320111(n) = if(n<=2, 1, my(p=A252463(n)); A001511(p)*A320111(A000265(p)));

CROSSREFS

Cf. A000005, A152822, A252463.

Cf. also A320107 and A319699, A319700, A319703, A319989.

Sequence in context: A196067 A251141 A319696 * A234287 A084294 A067752

Adjacent sequences:  A320108 A320109 A320110 * A320112 A320113 A320114

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Nov 22 2018

STATUS

approved

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Last modified October 21 16:50 EDT 2019. Contains 328302 sequences. (Running on oeis4.)