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A331740 Number of prime factors in A225546(n), counted with multiplicity. 5
0, 1, 2, 1, 4, 3, 8, 2, 2, 5, 16, 3, 32, 9, 6, 1, 64, 3, 128, 5, 10, 17, 256, 4, 4, 33, 4, 9, 512, 7, 1024, 2, 18, 65, 12, 3, 2048, 129, 34, 6, 4096, 11, 8192, 17, 6, 257, 16384, 3, 8, 5, 66, 33, 32768, 5, 20, 10, 130, 513, 65536, 7, 131072, 1025, 10, 2, 36, 19, 262144, 65, 258, 13, 524288, 4, 1048576, 2049, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

FORMULA

Additive with a(p^e) = A000120(e) * 2^(PrimePi(p)-1), where PrimePi(n) = A000720(n).

a(n) = A001222(A225546(n)).

A331591(n) <= a(n) <= A048675(n).

From Peter Munn, Sep 11 2021: (Start)

a(A001146(m)) = 1.

a(A331590(m, k)) = a(m) + a(k).

For squarefree k, a(k*m^2) = a(k) + a(m) = A048675(k) + a(m).

(End)

MATHEMATICA

Array[If[# == 1, 0, PrimeOmega@ Apply[Times, Flatten@ Map[Function[{p, e}, Map[Prime[Log2@ # + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]]] &, 75] (* Michael De Vlieger, Feb 08 2020 *)

PROG

(PARI) A331740(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, hammingweight(f[i, 2])*(2^(primepi(f[i, 1])-1))));

CROSSREFS

Cf. A000120, A000720, A001222, A048675, A225546, A331590.

Cf. also A331309, A331591.

Positions of 1's: A001146.

Sequence in context: A258863 A087207 A179206 * A074987 A294096 A128280

Adjacent sequences:  A331737 A331738 A331739 * A331741 A331742 A331743

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 05 2020

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)