A324723 -id:A324723 - cp's OEIS frontend

A324722 Numbers k such that A324658(A156552(k)) is zero.

9, 21, 25, 35, 49, 55, 77, 95, 121, 125, 133, 143, 169, 185, 203, 209, 221, 265, 289, 299, 301, 319, 323, 343, 361, 371, 377, 413, 427, 437, 445, 451, 473, 481, 493, 497, 511, 527, 529, 531, 539, 553, 559, 583, 589, 605, 611, 623, 629, 667, 679, 689, 703, 707, 737, 763, 767, 779, 791, 793, 799, 805, 817, 841, 845, 847, 851, 869, 871, 899, 901

Offset: 1

Antti Karttunen, Mar 15 2019

nonn

First even term is A005940(1+A324647(1)) = A005940(1+1116225) = 1912898. - Typo corrected by Antti Karttunen, Jul 21 2021

Antti Karttunen, Table of n, a(n) for n = 1..694 (based on Hans Havermann's factorization of A156552)
Index entries for sequences related to binary expansion of n
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to sigma(n)

Cf. A005940, A156552, A324647, A324652, A324658, A324723.

Positions of zeros in A324716.

isA324652(n) = ((2*n)==bitand(2*n, sigma(n)));
isA324722(n) = if(n>1,isA324652(A156552(n)));
k=0; n=0; while(k<105, n++; if(isA324722(n), k++; print1(n,", ")));

A324726 Numbers k such that 2k is equal to 2k OR sigma(k), where OR is bitwise-or, A003986, and sigma is the sum of divisors function.

Original entry on oeis.org

3, 6, 7, 14, 15, 21, 22, 28, 31, 46, 55, 57, 62, 63, 86, 92, 93, 94, 105, 110, 111, 124, 127, 154, 170, 171, 188, 189, 190, 201, 213, 215, 217, 231, 237, 248, 249, 250, 253, 254, 255, 310, 315, 316, 351, 357, 363, 369, 374, 376, 381, 382, 393, 430, 434, 447, 465, 469, 473, 483, 489, 494, 496, 497, 501, 506, 508, 511, 602

Offset: 1

Antti Karttunen, Mar 15 2019

Intersection with A324652 gives A000396.

These are all nonabundant (in A263837) because of the "monotonic property" of bitwise-or. - Antti Karttunen, Jan 08 2025

Cf. A000396, A003986, A318466, A324652, A324723, A324727 (the odd terms).

Subsequence of A263837.

Select[Range[1000], 2*# == BitOr[2*#, DivisorSigma[1, #]] &] (* Paolo Xausa, Mar 11 2024 *)

for(n=1, oo, if(((2*n)==bitor(2*n, sigma(n))), print1(n, ", ")));

{k such that 2*k = A318466(k)}.

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A324722 Numbers k such that A324658(A156552(k)) is zero.

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A324726 Numbers k such that 2k is equal to 2k OR sigma(k), where OR is bitwise-or, A003986, and sigma is the sum of divisors function.

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cp's OEIS Frontend

A324722 Numbers k such that A324658(A156552(k)) is zero.

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PARI

A324726 Numbers k such that 2*k is equal to 2*k OR sigma(k), where OR is bitwise-or, A003986, and sigma is the sum of divisors function.

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Author

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Mathematica

PARI

Formula

A324726 Numbers k such that 2k is equal to 2k OR sigma(k), where OR is bitwise-or, A003986, and sigma is the sum of divisors function.