A356349 -id:A356349 - cp's OEIS frontend

A363787 Primitive binary Niven numbers: binary Niven numbers (A049445) that are not twice another binary Niven number.

1, 6, 10, 18, 21, 34, 55, 60, 66, 69, 81, 92, 108, 115, 116, 126, 130, 155, 156, 172, 180, 185, 204, 205, 212, 222, 228, 246, 258, 261, 273, 284, 285, 295, 300, 308, 318, 321, 332, 340, 345, 355, 356, 366, 378, 395, 396, 404, 405, 414, 420, 425, 438, 452, 462

Offset: 1

Amiram Eldar, Jun 22 2023

Every binary Niven number is of the form m*2^k, where m is a term of this sequence and k >= 0.
Includes all the odd binary Niven numbers (A144302).
This sequence is infinite. E.g., 16^k + 4^k + 1 is a term for all k >= 1.

			6 is a term as 6 is a binary Niven number and 6/2 = 3 is not a binary Niven number.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A049445.
Disjoint union of A144302 and A363788.
A363789 is a subsequence.
Cf. A356349 (decimal analog).

binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; q[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]); Select[Range[500], q]

isbinniv(n) = !(n % hammingweight(n));
is(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));

A358255 Primitive Niven numbers ending with zero.

Original entry on oeis.org

110, 140, 150, 190, 220, 230, 280, 320, 330, 370, 410, 440, 460, 510, 550, 640, 660, 690, 730, 770, 780, 820, 870, 880, 910, 960, 990, 1010, 1040, 1050, 1090, 1130, 1160, 1180, 1220, 1230, 1270, 1300, 1310, 1360, 1380, 1410, 1450, 1540, 1590, 1630, 1680, 1720, 1740, 1770, 1810, 1860, 1890, 2020

Offset: 1

Bernard Schott, Nov 05 2022

A primitive Niven number (A356349) is a Niven number (A005349) that is not ten times another Niven number.
For any k > 0, there exist terms with k trailing zeros; for example R_2^k * 10^k (where R = A002275), so this sequence is infinite.
The smallest primitive Niven number ending with m zeros is A358256(m).

			150 is a term as 150 is a Niven number and 15 is not a Niven number.
180 is not a term as 180 is a Niven number but 18 is also a Niven number.

Giovanni Resta, Harshad numbers.

Cf. A002275, A005349.

Intersection of A008592 and A356349.

Select[10*Range[200], Divisible[#, (s = Plus @@ IntegerDigits[#])] && ! Divisible[#/10, s] &] (* Amiram Eldar, Nov 05 2022 *)

isniven(n) = n%sumdigits(n)==0; \\ A005349
isok(m) = !(m % 10) && isniven(m) && !isniven(m/10); \\ Michel Marcus, Nov 05 2022

A356350 Primitive terms of A357769: terms of A357769 that are not ten times another term of A357769.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 18, 24, 36, 48, 102, 108, 110, 112, 114, 126, 132, 140, 150, 156, 190, 204, 210, 216, 220, 224, 228, 230, 252, 264, 270, 280, 306, 312, 330, 336, 396, 408, 420, 440, 448, 460, 510, 540, 550, 624, 630, 660, 690, 756, 770, 840, 880

Offset: 1

Bernard Schott and Rémy Sigrist, Oct 15 2022

This sequence is infinite as it contains A133384.

Each term of A357769 can be uniquely written as a(m)*10^z for some m > 0 and z >= 0.

			230 is a term as 230 belongs to A357769 and 23 does not belong to A357769.
756 is a term as 756 belongs to A357769 and is not divisible by 10.

Index entries for sequences related to decimal expansion of n

Cf. A133384, A356349, A357769.

isA357769(n, base=10) = { my (d=digits(n, base), s=0); for (k=1, #d, if (n % (s+=d[k]), return (0)); ); return (1) }
is(n, base=10) = isA357769(n, base) && (n%base || !isA357769(n/base, base))

cp's OEIS Frontend

A363787 Primitive binary Niven numbers: binary Niven numbers (A049445) that are not twice another binary Niven number.

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A358255 Primitive Niven numbers ending with zero.

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A356350 Primitive terms of A357769: terms of A357769 that are not ten times another term of A357769.

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