A324105 - OEIS

A324105

a(1) = 0; for n > 1, a(n) = A000005(A156552(n)).

0, 1, 2, 2, 3, 2, 4, 2, 4, 3, 5, 2, 6, 2, 4, 4, 7, 2, 8, 2, 6, 4, 9, 2, 6, 4, 4, 4, 10, 4, 11, 2, 4, 4, 6, 4, 12, 2, 8, 4, 13, 2, 14, 2, 4, 8, 15, 2, 8, 3, 8, 2, 16, 2, 9, 2, 8, 6, 17, 2, 18, 4, 4, 6, 6, 4, 19, 4, 4, 2, 20, 4, 21, 4, 4, 4, 8, 4, 22, 2, 8, 4, 23, 6, 12, 8, 16, 8, 24, 6, 12, 4, 12, 12, 12, 4, 25, 3, 8, 4, 26, 6, 27, 2, 8

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OFFSET

1,3

COMMENTS

If a(n) is odd, then A067029(n) = 1 (and A319710(n) = 0), but not necessarily vice versa. See also formulas in A106737.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..4473

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

FORMULA

a(1) = 0; for n > 1, a(n) = A000005(A156552(n)).

MATHEMATICA

Array[If[# == 1, 0, DivisorSigma[0, #] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]]] &, 105] (* Michael De Vlieger, Mar 11 2019 *)

PROG

(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)};

A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));

A324105(n) = if(1==n, 0, numdiv(A156552(n)));

CROSSREFS

Cf. A000005, A067029, A106737, A156552, A319710, A324051.

Cf. also A323243, A324104, A324119, A324117 for similarly permuted sigma, phi, omega and A001227 (number of odd divisors).

Sequence in context: A335708 A076640 A326198 * A328871 A169819 A373738

Adjacent sequences: A324102 A324103 A324104 * A324106 A324107 A324108

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 18 2019

STATUS

approved