A325122 -id:A325122 - cp's OEIS frontend

A325120 Sum of binary lengths of the prime indices of n.

0, 1, 2, 2, 2, 3, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 5, 4, 4, 5, 4, 4, 5, 4, 4, 6, 5, 4, 5, 4, 5, 5, 4, 5, 6, 4, 5, 5, 5, 4, 6, 4, 5, 6, 5, 4, 6, 6, 5, 5, 5, 5, 7, 5, 6, 6, 5, 5, 6, 5, 5, 7, 6, 5, 6, 5, 5, 6, 6, 5, 7, 5, 5, 6, 6, 6, 6, 5, 6, 8, 5, 5, 7, 5, 5, 6

Offset: 1

Gus Wiseman, Mar 29 2019

nonn

The binary length of n is the number of digits in its binary representation. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Cf. A000120, A000720, A001222, A019565, A048881, A070939, A112798.
Cf. A325103, A325104, A325106, A325118, A325119.
Other totally additive sequences: A056239, A302242, A318994, A318995, A325033, A325034, A325121, A325122.

Table[Sum[pr[[2]]*IntegerLength[PrimePi[pr[[1]]],2],{pr,FactorInteger[n]}],{n,100}]

Totally additive with a(prime(n)) = A070939(n).

A325121 Sum of binary digits of the prime indices of n.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 1, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 1, 4, 2, 3, 2, 4, 4, 3, 3, 3, 2, 4, 3, 5, 3, 4, 3, 4, 2, 2, 3, 5, 3, 3, 3, 4, 4, 3, 4, 5, 2, 5, 4, 4, 1, 4, 4, 4, 2, 3, 2, 5, 2, 4, 3, 6, 4, 4, 3, 5, 3, 4, 2, 5, 3, 3, 5, 3, 3, 4, 3, 6, 4, 4, 4, 4, 5, 4, 3

Offset: 1

Gus Wiseman, Mar 29 2019

nonn

The sum of binary digits of an integer is the number of 1's in its binary representation. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Cf. A000120, A000720, A001222, A019565, A048881, A070939, A112798.
Cf. A325103, A325104, A325106, A325118, A325119.
Other totally additive sequences: A056239, A302242, A318994, A318995, A325033, A325034, A325120, A325122.

Table[Sum[pr[[2]]*DigitCount[PrimePi[pr[[1]]],2,1],{pr,FactorInteger[n]}],{n,100}]

Totally additive with a(prime(n)) = A000120(n).

cp's OEIS Frontend

A325120 Sum of binary lengths of the prime indices of n.

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