A368194 -id:A368194 - cp's OEIS frontend

A368195 a(n) is the number of numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the decimal expansion of n by one of the divisors of m.

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 7, 3, 6, 5, 8, 3, 9, 4, 6, 5, 6, 4, 11, 5, 8, 6, 10, 5, 8, 3, 8, 6, 7, 6, 13, 4, 8, 7, 8, 4, 11, 5, 10, 8, 9, 5, 15, 7, 6, 5, 8, 4, 11, 6, 12, 6, 8, 5, 12, 5, 8, 10, 12, 8, 14, 6, 12, 9, 8, 3, 13, 4, 7, 7, 10, 6, 12, 5, 10, 8

Offset: 1

Rémy Sigrist, Dec 16 2023

a(n) gives the number of terms in the n-th row of A368194.

			For n = 42: the 42nd row of A368194 contains 11 terms (1, 2, 3, 6, 7, 12, 14, 21, 22, 41, 42), so a(42) = 11.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
Index entries for sequences related to decimal expansion of n

Cf. A000005, A368194, A368314 (binary variant).

PARI
```
See Links section.
```

a(n) >= A000005(n).

A368313 Irregular table T(n, k), n > 0, k = 1..A368314(n), read by rows: the n-th row lists the numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the binary expansion of n by one of the divisors of m.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 2, 4, 1, 3, 5, 1, 2, 3, 6, 1, 3, 7, 1, 2, 4, 8, 1, 3, 5, 9, 1, 2, 5, 6, 10, 1, 3, 5, 7, 11, 1, 2, 3, 4, 6, 12, 1, 3, 5, 7, 13, 1, 2, 3, 6, 7, 14, 1, 3, 5, 7, 15, 1, 2, 4, 8, 16, 1, 3, 5, 9, 17, 1, 2, 3, 6, 9, 10, 18, 1, 3, 7, 9, 11, 19, 1, 2, 4, 5, 10, 12, 20

Offset: 1

Rémy Sigrist, Dec 21 2023

The n-th row starts with 1, ends with n, and contains the divisors of n (A027750).

			Table T(n, k) begins:
    1;
    1, 2;
    1, 3;
    1, 2, 4;
    1, 3, 5;
    1, 2, 3, 6;
    1, 3, 7;
    1, 2, 4, 8;
    1, 3, 5, 9;
    1, 2, 5, 6, 10;
    1, 3, 5, 7, 11;
    1, 2, 3, 4, 6, 12;
    1, 3, 5, 7, 13;
    1, 2, 3, 6, 7, 14;
    1, 3, 5, 7, 15;
    1, 2, 4, 8, 16;
    1, 3, 5, 9, 17;
    ...

Rémy Sigrist, Table of n, a(n) for n = 1..10177 (rows for n = 1..2^9 flattened)
Rémy Sigrist, PARI program
Index entries for sequences related to binary expansion of n

Cf. A027750, A368194 (decimal variant), A368314.

PARI
```
See Links section.
```

T(n, 1) = 1.

T(n, A368314(n)) = n.

A368198 a(n) gives the number of ways to go from n to 1 with steps consisting of replacing a positive number without leading zero, say m, appearing in the decimal expansion of a number, by a proper divisor of m.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 9, 2, 13, 4, 20, 2, 31, 4, 8, 4, 16, 7, 54, 10, 51, 10, 123, 16, 14, 2, 39, 7, 58, 9, 118, 5, 136, 17, 20, 6, 55, 16, 149, 25, 157, 19, 459, 44, 16, 5, 71, 8, 138, 12, 249, 13, 263, 18, 47, 8, 76, 33, 276, 35, 336, 26, 714, 87

Offset: 1

Rémy Sigrist, Dec 16 2023

			a(12) = 9 for we have nine ways to go from 12 to 1:
    12 -> 1,
    12 -> 2 -> 1,
    12 -> 3 -> 1,
    12 -> 4 -> 1,
    12 -> 4 -> 2 -> 1,
    12 -> 6 -> 1,
    12 -> 6 -> 2 -> 1,
    12 -> 6 -> 3 -> 1,
    12 -> 11 -> 1.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
Index entries for sequences related to decimal expansion of n

Cf. A368194, A368195, A368315 (binary variant).

PARI
```
See Links section.
```

a(1) = 1.

a(n) = Sum_{k = A368195(n)-1} a(A368194(k)) for any n > 1.

cp's OEIS Frontend

A368195 a(n) is the number of numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the decimal expansion of n by one of the divisors of m.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A368313 Irregular table T(n, k), n > 0, k = 1..A368314(n), read by rows: the n-th row lists the numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the binary expansion of n by one of the divisors of m.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A368198 a(n) gives the number of ways to go from n to 1 with steps consisting of replacing a positive number without leading zero, say m, appearing in the decimal expansion of a number, by a proper divisor of m.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula