A034090 -id:A034090 - cp's OEIS frontend

A281782 Numbers n such that sum of prime power divisors of n > sum of prime power divisors of m for all m < n.

2, 3, 4, 7, 8, 16, 27, 32, 64, 121, 125, 128, 243, 256, 512, 729, 1024, 2048, 4096, 6561, 8192, 15625, 16384, 32761, 32768, 59049, 65536, 117649, 130321, 131072, 177147, 262144, 524287, 524288, 1048576, 1594323, 1953125, 2097152, 4194304, 8388608

Offset: 1

Ilya Gutkovskiy, Apr 14 2017

nonn

Numbers n such that A023889(n) > A023889(m) for all m < n.

Numbers n such that Sum_{p^k|n, p prime, k>=1} p^k > Sum_{p^k|m, p prime, k>=1} p^k for all m < n.

Amiram Eldar, Table of n, a(n) for n = 1..65
Index entries for sequences related to sums of divisors

Cf. A002093, A002182, A023889, A034090, A174572, A246655, A280013.

mx = 0; t = {}; Do[u = DivisorSum[n, # &, PrimePowerQ[#] &]; If[u > mx, mx = u; AppendTo[t, n]], {n, 8500000}]; t

A185166 Number of prime divisors of n (counted with multiplicity) of numbers k such that sum of proper divisors of k exceeds that of all smaller numbers.

Original entry on oeis.org

0, 1, 2, 2, 3, 2, 3, 3, 3, 4, 3, 4, 5, 4, 5, 4, 4, 6, 5, 5, 6, 5, 5, 6, 6, 7, 5, 6, 6, 5, 7, 6, 6, 6, 5, 7, 6, 8, 7, 7, 7, 6, 8, 6, 7, 6, 6, 8, 6, 8, 7, 9, 7, 8, 8, 8, 7, 7, 7, 9, 6, 7, 8, 7, 7, 7, 9, 9, 8, 8, 7, 9, 7, 8, 8, 8, 7, 9, 7, 9, 8, 8, 10, 8, 9, 9, 9

Offset: 1

Jonathan Vos Post, Feb 19 2011

nonn

			a(1) = 0 because 1 = A034090(1) has no prime factors.
a(2) = 1 because 2 = A034090(2) has one prime factor, itself.
a(3) = 2 because 4 = A034090(3) = 2^2 has two prime factors (with multiplicity).

Amiram Eldar, Table of n, a(n) for n = 1..1000 (calculated from the b-file at A034090)

Cf. A001222, A034090, A001065, A034091, A034287, A034288.

a(n) = A001222(A034090(n)).

More terms from Amiram Eldar, Aug 30 2019

A279091 Numbers k for which sigma(k) - 4k exceeds sigma(j) - 4j for all j < k.

Original entry on oeis.org

1, 27720, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 360360, 443520, 471240, 498960, 554400, 655200, 665280, 720720, 942480, 1053360, 1081080, 1330560, 1413720, 1441440, 1663200, 1801800, 1884960, 2106720, 2162160, 2827440, 2882880, 3326400

Offset: 1

Jon E. Schoenfield, Jan 30 2017

nonn

Does lcm(1..10) = 2520 divide a(n) for all n > 1?

Does lcm(1..11) = 27720 divide a(n) for all n except 1, 3, and 16?

			50400 is in the sequence because sigma(50400) - 4*50400 = 203112 - 201600 = 1512, and no k < 50400 has a value of sigma(k) - 4k this large.

Michel Marcus, Table of n, a(n) for n = 1..77

Cf. A034090, A140522, A279088: with 1, 2 and 3 instead of 4.

lista(nn) = {m = -oo; k = 0; for (n=1, nn, if ((nm = (sigma(n) - 4*n)) > m, k++; print1(n, ", "); m = nm););} \\ Michel Marcus, Nov 02 2017

A290490 Numbers k such that (sum of proper unitary divisors of k) > (sum of proper unitary divisors of m) for all m < k.

Original entry on oeis.org

1, 2, 6, 10, 14, 18, 22, 26, 30, 42, 60, 66, 78, 102, 114, 138, 150, 174, 186, 210, 330, 390, 462, 510, 546, 570, 690, 798, 858, 870, 930, 1050, 1110, 1218, 1230, 1290, 1410, 1470, 1590, 1722, 1770, 1830, 2010, 2130, 2190, 2310, 2730, 3570, 3990, 4290, 4830, 5610, 6006, 6090, 6510, 7410, 7590, 7770

Offset: 1

Ilya Gutkovskiy, Aug 03 2017

nonn

Numbers k such that A034460(k) > A034460(m) for all m < k.

Amiram Eldar, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Unitary Divisor
Index entries for sequences related to sums of divisors

Cf. A002182, A002093, A034090, A034448, A034460, A063919, A280013, A281782, A285614.

mx = -1; t = {}; Do[u = DivisorSum[n, # &, GCD[#, n/#] == 1 &] - n; If[u > mx, mx = u; AppendTo[t, n]], {n, 8000}]; t

sumud(n) = sumdiv(n, d, if (gcd(d, n/d)==1, d)) - n;
lista(nn) = {lasts = -1; for (n=1, nn, if ((news = sumud(n)) > lasts, print1(n, ", "); lasts = news););} \\ Michel Marcus, Aug 04 2017

cp's OEIS Frontend

A281782 Numbers n such that sum of prime power divisors of n > sum of prime power divisors of m for all m < n.

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A185166 Number of prime divisors of n (counted with multiplicity) of numbers k such that sum of proper divisors of k exceeds that of all smaller numbers.

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A279091 Numbers k for which sigma(k) - 4k exceeds sigma(j) - 4j for all j < k.

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A290490 Numbers k such that (sum of proper unitary divisors of k) > (sum of proper unitary divisors of m) for all m < k.

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