A351559 - OEIS

A351559

a(n) = A048675(gcd(sigma(n), A019565(n))).

0, 2, 1, 0, 1, 2, 1, 0, 0, 2, 3, 8, 9, 2, 3, 0, 1, 2, 1, 0, 1, 2, 3, 0, 0, 10, 1, 8, 5, 2, 1, 0, 1, 2, 3, 32, 1, 6, 1, 0, 9, 2, 1, 8, 33, 2, 3, 0, 0, 2, 3, 0, 1, 6, 3, 0, 1, 2, 3, 8, 1, 2, 33, 0, 1, 2, 65, 0, 1, 2, 3, 0, 1, 2, 1, 12, 1, 10, 5, 0, 16, 2, 3, 0, 1, 18, 7, 0, 1, 2, 9, 8, 1, 2, 7, 0, 1, 2, 35, 0, 65, 2, 33

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OFFSET

1,2

LINKS

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

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

FORMULA

a(n) = A048675(A351557(n)) = A048675(gcd(sigma(n), A019565(n))).

a(n) = n AND A351560(n), where AND is bitwise-and, A004198.

MATHEMATICA

Table[If[# == 1, 0, Total[#2*2^PrimePi[#1] & @@@ FactorInteger[#]]/2] &@ GCD[DivisorSigma[1, n], Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 103}] (* Michael De Vlieger, Feb 20 2022 *)

PROG

(PARI)

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

A351559(n) = A048675(gcd(sigma(n), A019565(n)));

CROSSREFS

Cf. A000203, A004198, A007947, A019565, A080398, A351557, A351560.

Cf. also A324644, A351558.

Sequence in context: A170968 A114114 A090787 * A229707 A262680 A366128

Adjacent sequences: A351556 A351557 A351558 * A351560 A351561 A351562

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Feb 19 2022

STATUS

approved