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A336931 Difference between the 2-adic valuation of A003973(n) [= the sum of divisors of the prime shifted n] and the 2-adic valuation of the number of divisors of n. 4
0, 1, 0, 0, 2, 1, 1, 1, 0, 3, 0, 0, 0, 2, 2, 0, 1, 1, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 4, 3, 0, 1, 0, 2, 3, 0, 0, 3, 0, 3, 1, 2, 3, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 2, 2, 2, 5, 0, 2, 1, 1, 1, 0, 2, 1, 2, 1, 0, 4, 0, 1, 3, 1, 0, 2, 1, 1, 1, 2, 0, 2, 0, 1, 3, 4, 4, 1, 0, 3, 1, 0, 0, 1, 4, 1, 0, 1, 0, 0, 2, 2, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Note that A295664(n) = A295664(A003961(n)).

LINKS

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

FORMULA

Additive with a(p^e) = 0 when e is even, a(p^e) = A007814(1+A003961(p))-1 when e is odd.

a(n) = A336932(n) - A295664(n).

a(n) = a(A007913(n)).

PROG

(PARI)

A007814(n) = valuation(n, 2);

A336931(n) = { my(f=factor(n)); sum(i=1, #f~, (f[i, 2]%2) * (A007814(1+nextprime(1+f[i, 1]))-1)); };

(PARI)

A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };

A007814(n) = valuation(n, 2);

A336931(n) = (A007814(A003973(n)) - A007814(numdiv(n)));

CROSSREFS

Cf. A003961, A003973, A007814, A007913, A295664, A336930 (positions of zeros), A336932, A336937.

Sequence in context: A089339 A249303 A319081 * A182662 A308778 A127284

Adjacent sequences:  A336928 A336929 A336930 * A336932 A336933 A336934

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 17 2020

STATUS

approved

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)