A342555 2*a(n) is the start of 3 consecutive numbers (even-odd-even) that are sums of divisors, i.e., terms of A000203.

3, 6, 15, 19, 63, 153, 199, 255, 423, 480, 511, 546, 861, 1111, 1189, 1400, 1770, 1875, 1935, 1995, 2047, 2556, 3475, 3619, 4005, 4095, 4920, 5151, 5215, 6649, 8046, 8191, 8646, 8749, 9765, 11175, 11199, 14028, 14197, 15391, 15427, 15470, 16383, 19494, 25878, 26557, 26799

Offset: 1

Author

Hugo Pfoertner, May 14 2021

Keywords

• nonn

Comments

There exists one exceptional case of 4 consecutive numbers 12, 13, 14, 15, where 13 would start an odd-even-odd progression.

Examples

			a(1) = 3, because 2*3 = 6 is the start of the first occurrence of a row of 3 consecutive numbers, all of which are in A000203. 6 = sigma(5), 7 = sigma(4), 8 = sigma(7).
a(2) = 6: 2*6 = 12 = sigma(6) = sigma(11), 13 = sigma(9), 14 = sigma(13). 15 = sigma(8), which would be at the end of the row 13, 14, 15, is excluded by the even-odd-even condition.
a(3) = 15: 2*15 = 30 = sigma(29), 31 = sigma(16) = sigma(25), 32 = sigma(21) = sigma(31).
See Jeppe Stig Nielsen's list for more examples.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..1000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp, Oct. 2005.
• Jeppe Stig Nielsen, List of numbers with divisor sum k, k<=10000.

Crossrefs

Cf. A000203, A085790, A342560.

Programs

PARI

a342555(nterms) = {my(N=vector(3, i, invsigmaNum(i+1)), n=0, k=4); while(n<=nterms, if(vecmin(N)>0 && !(k%2), print1((k-2)/2, ", "); n++); k++; N[1+k%3] = invsigmaNum(k))}; \\ see Alekseyev link for invsigmaNum()
a342555(46)